  For each n\geq 1 we introduce two new Segal-type models of n-types of
topological spaces: weakly globular n-fold groupoids, and a lax version of
these. We show that any n-type can be represented up to homotopy by such models
via an explicit algebraic fundamental n-fold groupoid functor. We compare these
models to Tamsamani's weak n-groupoids, and extract from them a model for
(k-1)connected n-types
