Let G be an Abelian group with a metric d and E be a normed space. For any f : G → E we define the Drygas difference of the function f by the formula
for all x, y ∈ G. In this article, we prove that if ˄f is Lipschitz, then there exists a Drygas function D : G → E such that f − D is Lipschitz with the same constant. Moreover, some results concerning the approximation of the Drygas functional equation in the Lipschitz norms are presented.