Distance properties of trellis codes are of great importance for performance evaluation. In this paper, we use random coding analysis to study the average distance structures of trellis codes. The generating function enumerating the average number of error events of each distances is fully determined in the ensemble of time-varying trellis codes. The results obtained can be used to predict the growth rate of the number of error events at large distance and hence determine the signal-to-noise range in which the transfer function bound for error performance is convergent. Other applications of the average distance structure include a Gilbert-type lower bound on minimum distance.