In this paper, we extend the concept of the group ${varepsilon}(X)$ of self homotopy equivalences of a space X to that of an object in the category of pairs. Mainly, we study the group ${varepsilon}(X,;A)$ of pair homotopy equivalences from a CW-pair (X, A) to itself which is the special case of the extended concept. For a CW-pair (X, A), we find an exact sequence $1;{ o};G;{ o};{varepsilon}(X,;A);{to};{varepsilon}(A)$ where G is a subgroup of ${varepsilon}(X,;A)$. Especially, for CW homotopy associative and inversive H-spaces X and Y, we obtain a split short exact sequence $1;{ o};{varepsilon}(X);{ o};{varepsilon}(X{ imes}Y,Y);{ o};{varepsilon}(Y);{ o};1$ provided the two sets $[X{wedge}Y,;X{ imes}Y]$ and [X, Y] are trivial.