The famous Oseledets theorem states that if $g_n$ is a stationary sequence of $m\times m$ matrices then with probability 1 there is a (random) basis in ${\mathbb{R}}^m$ such that for any vector $x$ the asymptotic behaviour of $||g_n...g_1x||$ is the same as that for one of the vectors from this basis. The fact that the sequence is stationary is crucial for the existence of such a basis. I shall consider the case when the sequence is not stationary. It turns out that for independent non-identically distributed matrices one can still obtain an analogue of the Oseledets's results. Some applications will be considered.