The authors develop some general theory of homogeneous spaces, generated by morphisms of G-spaces. The initial notion is a global pair (G,A), where G is a Lie group and \(A\subset End(G)\) is a set of its endomorphisms. The authors associate with a global pair (G,A) a group \(G_ 0=Map(A,G)\) of maps \(A\to G\) with natural endomorphism \(\gamma\) : \(G_ 0\to G_ 0\), \[ \gamma (f)(\phi)=\phi (f(\phi)),\quad \phi \in A,\quad f\in G_ 0. \] In the case of a finite set \(A=\{\phi_ 1,...,\phi_ n\}\), \(G_ 0=G\times...\times G,\gamma =\phi_ 1\circ...\circ \phi_ n.\) Some homogeneous spaces of Lie groups G and \(G_ 0\) are defined and studied. The case when G is a semidirect product of Lie groups is considered in more detail. In the particular case when G is the affine group \(GL(n,{\mathbb{R}})\cdot {\mathbb{R}}^ n\) and the set A consists of two automorphisms, an interpretation of homogeneous spaces associated with the pair (G,A) is given in terms of affine geometry.