One of the important to the filed of economic growth problems refers to the issue of convergence and catching-up of less developed and efficient countries with their more developed and efficient counterparts. In this study, we investigate convergence of two groups of Transition Economies (TE) in terms of the productive efficiency of utilization of investments in Telecoms and generation of revenues from Telecoms. We use Malmquist Index of input- and output-oriented Data Envelopment Analysis (DEA) to obtain values in changes in Total Factor Productivity (TFP) of 18 TEs over the period from 1993 to 2002. After comparison of the averaged values of Malmquist index for two groups, we were able to reject null hypotheses of no convergence.