Homogeneity and h-homogeneity

The relations between zero-dimensional homogeneous spaces and h-homogeneous ones are investigated. We suggest an indication of h  -homogeneity for a homogeneous zero-dimensional paracompact space and its modification for a topological group. We describe some cases when the product X×YX×Y is an h-homogeneous space provided X is h-homogeneous and Y is homogeneous.