In this paper we study stochastic comparisons and dependence propefties for the epoch and inter-epoch times of trend renewal processes with different trend functions. These results extend some of the results on the non-homogeneous Poisson process in Belzunce et al. (2001, 2003) to trend renewal processes. Some applications of the results to a shock model, a repair process, and a specific class of intermediate order statistics are provided. (C) 2018 Elsevier Inc. All rights reserved.