  We prove, under different natural hypotheses, that the random
multidimensional affine recursion $X_n=A_nX_{n-1}+B_n\in\mathbb{R}^d, n \geq
1,$ is recurrent in the critical case. In particular we cover the cases where
the matrices $A_n$ are similarities, invertible, rank 1 or with non negative
coefficients.
  These results are a consequence of a criterion of recurrence for a large
class of affine recursions on $\mathbb R^d$, based on some moment assumptions
of the so-called ``reverse norm control random variable".
