The purpose of this paper is the study of CS-regular maps in the realm of quasi-pseudo metric spaces (asymmetric spaces). Some theorems on extensions of these maps to the bicompletion in separated quasi-pseudo metric spaces are presented. The class of uniformly continuous maps with respect to the metric is properly contained in the class of CS-regular maps. Important maps which occur in analysis are CS-regular but not necessarily uniformly continuous. The problem of extensions of CS-regular maps from a dense subset of a metric space to the whole space has been solved long ago.