What passage are you reading? Both μέν and δέ can occur by themselves, They don't have to occur together. When they do occur together, sometimes the position of δέ is not always the second in the clause (see below). You can get access to Smyth's Greek Grammar for Colleges at http://perseus.uchicago.edu/cgi-bin/philologic/navigate.pl?NewPerseusMonographs.9
. In addition, the δέ clause may be only suggested. Here are some relevant articles:
Smyth §2914. Position of μέν (and δέ).—μέν and δέ are commonly placed next to the words they contrast, and take precedence over other postpositive particles. But when two words belong closely together, μέν and δέ are placed between. Thus, when nouns with the article are contrasted, μέν and δέ stand after the article; it the nouns depend on prepositions μέν and δέ stand after the preposition and before the article.
a. But this rule may be neglected in order to emphasize the preceding word, as τὰ μὲν ἀνθρώπινα παρέντες, τὰ δαιμόνια δὲ σκοποῦντες neglecting human affairs, but speculating on things divine X. M. 1. 1. 12, ἀνὰ τὸ σκοτεινὸν μέν in the darkness T. 3. 22.
b. If the noun has no article and is governed by a preposition, δέ usually takes the third place.
c. Postponement of δέ (and some other postpositive particles) to the fourth place is only apparent after an introductory vocative, which is not regarded as forming an integral part of the sentence.
2915. μέν and δέ are sometimes referred to the entire clause or to the predicate and not to the words that are opposed to each other. This arrangement is often adopted to preserve the symmetry of the juxtaposed clause. μέν and δέ are thus often placed after personal or demonstrative pronouns. Thus, ἔλεγε μὲν ὡς τὸ πολύ, τοῖς δὲ βουλομένοις ἐξῆν ἀκούειν Socrates for the most part was wont to talk, while any who chose could listen X. M. 1. 1. 10, πῶς ἂν πολλοὶ μὲν ἐπεθῡ́μουν τυραννεῖν …; πῶς δὲ πάντες ἐζήλουν ἂν τοὺς τυράννους; why should many desire to possess despotic power? why should everybody envy despotic rulers? X. Hi. 1. 9 (for πάντες δὲ πῶς ἐζήλουν ἄν). Cp. ἐν μὲν τούτοις … ἐν ἐκείνοις δέ Lyc. 140, περὶ αὑτῶν μὲν … περὶ δὲ τῶν δεσποτῶν L. 7. 35, etc.
a. The transposition is often designed to produce a chiastic (3020) order, as ἔπαθε μὲν οὐδέν, πολλὰ δὲ κακὰ ἐνόμιζε ποιῆσαι he suffered no loss, but thought that he had done a great deal of damage X. A. 3. 4. 2 (here οὐδέν and πολλά are brought close together).
2916. In poetry μέν and δέ often have a freer position than in prose. δέ may often come third when an emphatic word is placed before it, and even fourth.
Smyth, H. W. (1920). A Greek Grammar for Colleges (657). New York; Cincinnati; Chicago; Boston; Atlanta: American Book Company..
① marker of correlation, w. other particles
ⓐ introducing a concessive clause, followed by another clause w. an adversative particle: to be sure … but, on the one hand … on the other hand, though in many cases an equivalence translation will not fit this scheme; rather, the contrast is to be emphasized in the second clause, often with but.
α. μὲν … δέ: ἐγὼ μὲν ὑμᾶς βαπτίζω … ὁ δὲ ὀπίσω μου ἐρχόμενος Mt 3:11. ὁ μὲν θερισμὸς … οἱ δὲ ἐργάται 9:37. τὸ μὲν ποτήριόν μου πίεσθε … τὸ δὲ καθίσαι 20:23. ὁ μὲν υἱὸς τοῦ ἀνθρώπου … οὐαὶ δὲ τῷ ἀνθρώπῳ ἐκείνῳ Mk 14:21. τοῦ μὲν πρώτου κατέαξαν τὰ σκέλη … ἐπὶ δὲ τὸν Ἰησοῦν ἐλθόντες J 19:32 and oft. Cp. Mt 22:8; Ac 21:39; Ro 6:11; 1 Cor 9:24; 11:14; 12:20; 2 Cor 10:10; Hb 3:5; 1 Pt 1:20.—In combination w. conjunctions: εἰ μὲν … εἰ δέ if … but if Dg 3:2 (TestJob 23:5; Ar. 13:7). εἰ μὲν οὖν … εἰ δέ if then … but if Ac 19:38; cp. 25:11. εἰ μὲν … νῦν δέ if … but now Hb 11:15. μὲν οὖν … δέ (now) indeed … but J 19:24; 20:30; Ac 8:4; 12:5; 1 Cor 9:25. μὲν γὰρ … δέ/ἀλλά for indeed … but (Wsd 7:30; Job 28:2; 2 Macc 6:4; 7:36; 4 Macc 9:8f, 31f) Ac 13:36f; 23:8; 28:22; Ro 2:25; 1 Cor 5:3; 11:7; 2 Cor 9:1–3; 11:4; Hb 7:18, 20f; 12:10; Ac 28:22 (in reverse order): also ἀλλά for δέ in apodosis 4:16f (as 3 Macc 2:15f), s. β. κἂν μὲν … , εἰ δὲ μήγε if … but if not Lk 13:9. ἐὰν μὲν … , ἐὰν δὲ μή Mt 10:13. W. prep. εἰς μὲν … εἰς δέ Hb 9:6.
ⓒ Somet. the combination μὲν … δέ does not emphasize a contrast, but separates one thought from another in a series, so that they may be easily distinguished: πρῶτον μὲν … ἔπειτα δέ in the first place … then Hb 7:2. ὃ μὲν … ὃ δέ the one … the other Mt 13:8, 23 (cp. Lucian, Hermot. 66 ὁ μὲν ἑπτά, ὁ δὲ πέντε, ὁ δὲ τριάκοντα; Just., D. 35, 6; 39, 2; cp. TestAbr A 10 p. 87, 21 [Stone p. 22] ἄλλους μὲν … ἑτέρους); Ro 9:21. ὃς μὲν … ὃς δέ the one … the other Mt 21:35; 25:15; Lk 23:33; Ac 27:44; Ro 14:5; 1 Cor 11:21; Jd 22. ἃ μὲν … ἃ δέ some … others 2 Ti 2:20. ὁ μὲν … ὁ δέ the one … the other, but pl. some … others Ac 14:4; 17:32; Gal 4:23; Eph 4:11; Phil 1:16; Dg 2:2f. ἕκαστος … , ὁ μὲν οὕτως ὁ δὲ οὕτως each one … , one in one way, one in another 1 Cor 7:7. ὃς μὲν πιστεύει φαγεῖν πάντα, ὁ δὲ ἀσθενῶν the one is confident about eating anything, but the weak person Ro 14:2. τινὲς μὲν … τινὲς δέ some … but still others Phil 1:15. ἄλλη μὲν …, ἄλλη δὲ …, ἄλλη δέ … 1 Cor 15:39. ἑτέρα μὲν …, ἑτέρα δέ vs. 40. οἱ μὲν … , ἄλλοι δὲ … , ἕτεροι δέ Mt 16:14. ᾧ μὲν γὰρ … , ἄλλῳ δὲ … , ἑτέρῳ 1 Cor 12:8ff. ἃ μὲν … , ἄλλα δὲ … , ἄλλα δέ Mt 13:4ff. τοῦτο μὲν … , τοῦτο δέ in part … in part (Hdt. 3, 106; Isocr. 4, 21; 22) Hb 10:33 (μέν followed by more than one δέ: two, Libanius, Or. 18, p. 251, 3f; Or. 59 p. 240, 13; four, Or. 64 p. 469, 14).
② marker of contrast or continuation without express correlation and frequently in anacolutha
ⓐ when the contrast can be supplied fr. the context, and therefore can be omitted as obvious: λόγον μὲν ἔχοντα σοφίας (sc. ὄντα δὲ ἄλογα or someth. sim.) they have the reputation of being wise (but are foolish) Col 2:23 (difft. BHollenbach, NTS 25, ’79, 254–61: a subordinate clause embedded in its main clause). τὰ μὲν σημεῖα τοῦ ἀποστόλου κατειργάσθη ἐν ὑμῖν the signs that mark a true apostle were performed among you (but you paid no attention) 2 Cor 12:12. ἤδη μὲν οὖν ἥττημα indeed it is already a defeat for you (but you make it still worse) 1 Cor 6:7.—μέν serves to emphasize the subject in clauses which contain a report made by the speaker’s personal state of being, esp. intellectual or emotional; so ἐγὼ μ. Παῦλος 1 Th 2:18. ἡ μ. εὐδοκία τῆς ἐμῆς καρδίας Ro 10:1.
ⓑ Somet. the contrast is actually expressed, but not in adversative form (Diod S 12, 70, 6 Ἀθηναῖοι μὲν οὖν ἐπιβουλεύσαντες τοῖς Βοιωτοῖς τοιαύτῃ συμφορᾷ περιέπεσον=so the Ath., one can see, after plotting against the B., had their fortunes reversed in such a disaster; Polyaenus with dramatic effect: 4, 3, 20 οἱ μὲν … , Ἀλέξανδρος … ; 2, 3, 2) τότε μὲν … ἔπειτα (here we expect δέ) J 11:6f. ἐφʼ ὅσον μὲν οὖν εἰμι ἐγὼ ἐθνῶν ἀπόστολος in so far, then, as I am an apostle to the nations Ro 11:13 (the contrast follows in vs. 14); cp. 7:12 and 13ff.
ⓒ We notice anacoluthon in enumerations, either if they are broken off or if they are continued in some manner that is irregular in form: πρῶτον μέν in the first place Ro 1:8; 3:2; 1 Cor 11:18. πρῶτον μὲν … ἔπειτα (X., Cyr. 7, 5, 1) Js 3:17. In the prologue to Ac (s. λόγος 1b) the clause w. δέ corresponding to τὸν μὲν πρῶτον λόγον 1:1 (Diod S 11, 1, 1 ῾Η μὲν οὖν πρὸ ταύτης βίβλος … τὸ τέλος ἔσχε τῶν πράξεων … ἐν ταύτῃ δέ … The preceding book … contained … ; in this one, on the other hand … ) may have been omitted through editorial activity acc. to Norden, Agn. Th. 311ff; 397.
Arndt, W., Danker, F. W., & Bauer, W. (2000). A Greek-English lexicon of the New Testament and other early Christian literature (3rd ed.) (630). Chicago: University of Chicago Press.