The transient stability analysis is the most time‐consuming computer simulation in power system studies. For this reason, in recent years, parallel processing has been applied for implementing on‐line time‐domain simulations of power system transient behaviour. As is well known, the problem of power system transient simulation consists, basically, in the solution of an initial value problem for a mixed set of Ordinary Differential Equations (ODE) and algebraic equations. The objective of this paper is to present an algorithm based on Shifted‐Picard dynamic iterations, which solves the above mentioned set of non‐linear Differential Algebraic Equations (DAE) by the iterative solution of a linear set of DAE. This feature is important because the time behaviour of the linear set of differential equations can be obtained by the solution of an integral. In this case, a multiprocessor parallel‐in‐time implementation of such algorithms is possible because each processor is devoted to the evaluation of the required variables relative to each time step. Moreover, parallelism‐in‐time allows multigrid techniques to be implemented in a natural way. Test results on realistic‐sized power systems are presented.