Меры на сокрушающих произведениях квазигрупп и их алгебры

We study quasiinvariant measures on smashed and twisted wreath products of quasigroups. The quasiinvariance of measures is investigated relative to isotopies. Specific features are found for quasigroups in comparison with groups. Spaces of measures are scrutinized. Convolution algebras appear to be in general nonassociative because of the nonassociativity of the quasigroup. Ideals of topological convolution algebras are studied