Speech accommodation happens when two people engage in verbal conversation. In this paper two types of accommodation are investigated – one dependent on cognitive, physiological, functional and social constraints (Convergence), the other dependent on linguistic and paralinguistic factors (Synchrony). Convergence refers to the situation when two speakers' speech characteristics move towards a common point. Synchrony happens if speakers' prosodic features become correlated over time. Here we analyze relations between the two phenomena at the single word level. Although calculation of Synchrony is fairly straightforward, measuring Convergence is even more problematic as proved by a long history of debates on how to define it. In this paper we consider Convergence as an emergent behavior and investigate it by developing a robust and automatic method based on Gaussian Mixture Model (GMM). Our results show that high Synchrony of F0 between two speakers leads to greater amount of Convergence. This provides robust support for the idea that Synchrony and Convergence are interrelated processes, particularly in female participants.