  We describe an algorithm for computing successive quotients of the Schur
multiplier $M(G)$ for a group $G$ given by an invariant finite
$L$-presentation. As application, we investigate the Schur multipliers of
various self-similar groups such as the Grigorchuk super-group, the generalized
Fabrykowski-Gupta groups, the Basilica group and the Brunner-Sidki-Vieira
group.
