I did some work last week on the use of αρχωομαι+ Infv. as an apparent substitute for the imperfect tense form. In each case that Mark uses this combination, Luke does something else, either aorist or imperfect form of a semantically similar verb to Mark’s infv. However, one finds a number of instances where Luke himself uses ARXWΟΜΑΙ + Infv., but they are in contexts where there is no synoptic parallel. So for those that might want to claim that this usage is more bad grammar on Mark’s part, time to go back to the drawing board. Or else, one might claim that Q uses bad grammar as well.  😉 A PDF of the syntax search results from OpenText.org in Libronix are available as a PDF here, about six pages.

Below are some representative examples of the apparent change that I am talking about, depending on how you handle the synoptic issues. Matthew’s version has some differences, but follows the mood and tense of Mark. Luke’s version uses the imperfect indicative to express the infinitival action.

Mark 2:23 καὶ ἐγένετο αὐτὸν ἐν τοῖς σάββασιν παραπορεύεσθαι διὰ τῶν σπορίμων καὶ οἱ μαθηταὶ αὐτοῦ ἤρξαντο ὁδὸν ποιεῖν τίλλοντες τοὺς στάχυας Luke 6:1 Ἐγένετο δὲ ἐν σαββάτῳ διαπορεύεσθαι αὐτὸν διὰ σπορίμων, καὶ ἔτιλλον οἱ μαθηταὶ αὐτοῦ καὶ ἤσθιον τοὺς στάχυας ψώχοντες ταῖς χερσίν.Matt 12:1b καὶ ἤρξαντο τίλλειν στάχυας καὶ ἐσθίειν.

This next example illustrates again Luke’s use of the imperfect in the same context that Mark uses the infinitival construction. It really doesn’t matter whether Luke “changed” his version or composed it. The point is he chose the imperfect for the comparable discourse context. Matthew goes his own way, using an indicative instead of the infinitive construction, but opts for aorist.

Mark 5:17  καὶ ἤρξαντο παρακαλεῖν αὐτὸν ἀπελθεῖν ἀπὸ τῶν ὁρίων αὐτῶν Luke 8:31  καὶ παρεκάλουν αὐτὸν ἵνα μὴ ἐπιτάξῃ αὐτοῖς εἰς τὴν ἄβυσσον ἀπελθεῖν.

Matt 8:34b  καὶ ἰδόντες αὐτὸν παρεκάλεσαν ὅπως μεταβῇ ἀπὸ τῶν ὁρίων αὐτῶν.

The final example is taken from the rejection of Jesus in Nazareth, his home town. The focus is on verse 2 of Mark 6, but v. 1 is supplied for context. There really is no specific counterpart in Luke, but Matthew’s version sports an imperfect.

Mark 6:1-2  Καὶ ἐξῆλθεν ἐκεῖθεν καὶ ἔρχεται εἰς τὴν πατρίδα αὐτοῦ, καὶ ἀκολουθοῦσιν αὐτῷ οἱ μαθηταὶ αὐτοῦ. 2 καὶ γενομένου σαββάτου ἤρξατο διδάσκειν ἐν τῇ συναγωγῇ, καὶ πολλοὶ ἀκούοντες ἐξεπλήσσοντο λέγοντες Matt 13:54  καὶ ἐλθὼν εἰς τὴν πατρίδα αὐτοῦ ἐδίδασκεν αὐτοὺς ἐν τῇ συναγωγῇ αὐτῶν, ὥστε ἐκπλήσσεσθαι αὐτοὺς καὶ λέγειν, Πόθεν τούτῳ ἡ σοφία αὕτη καὶ αἱ δυνάμεις;

And about the time you think there may be an pattern emerging, reality strikes. In the section that Luke adds which includes the OT quotation, he uses the same infinitival construction found in Mark to introduce Jesus speech, for which there is no synoptic parallel.

Luke 4:21  ἤρξατο δὲ λέγειν πρὸς αὐτοὺς ὅτι Σήμερον πεπλήρωται ἡ γραφὴ αὕτη ἐν τοῖς ὠσὶν ὑμῶν.

If anyone is looking for a research topic, here you go. I would suggest taking Luke’s usage as expressing the preferred one, and try to contrast it with the places in Mark that it is changed. There may be some mitigating constraint that makes Mark’s usage dispreferred, “What not to do” as it were, but this is just a hunch. One would also want to look for comparable usage by Koine writers to test the hypothesis.