In this paper we study the impact of the simultaneous exploitation of data-- and task--parallelism on Strassen and Winograd matrix multiplication algorithms. We present two mixed--parallel implementations. The former follows the phases of the original algorithms while the latter has been designed as the result of a list scheduling algorithm. We give a theoretical comparison- , in terms of memory usage and execution time, between our algorithms and classical data--parallel implementations. This analysis is corroborated by experiments. Finally we give some hints about an heterogeneous version of our algorithms.