  This paper studies the formal deformations of differential algebra morphisms.
As a consequence, we develop a cohomology theory of differential algebra
morphisms to interpret the lower degree cohomology groups as formal
deformations. Then, we prove the Cohomology Comparison Theorem of differential
algebra morphisms, i.e., the cohomology of a morphism of differential algebras
is isomorphic to the cohomology of an auxiliary differential algebra. Finally,
we can give a minimal model for morphism of differential algebras with
weight=0.
