In this talk we will consider convergence of series of independent stochastic processes with cadlag paths (cadlag means right-continuous with left-hand limits). For symmetric processes, we show that finite dimensional convergence to a cadlag limit implies uniform convergence almost surely, and thereby extend the Ito-Nisio Theorem to the Skorokhod space D[0,1]. The above result is used to show uniform convergence of the series representation of cadlag infinitely divisible processes which, in particular, implies convergence of corresponding jump processes. The talk is based on joint work with Jan Rosinski, The University of Tennessee, USA.