A class of models with non-abelian gauge invariance called HP n−1 (they are a generalization of the abelian CP n−1 models) is considered at the quantum level, in particular in view of their relation with the O( n) non-linear σ-models, which is connected with the confinement property. Renormalization, critical behaviour and the 1 n expansion are studied in 2 or 2 + ϵ dimensions. A comparison between the abelian CP n−1 and the non-abelian HP n−1 allows us to discuss the rôle of the classical solutions in the confinement problem.