Abstract: The first part of this paper discuses the obligue derivative boundary value problem for the generalized regular function with value in Quaternions. We got the existence and uniqueness of the solution of the problem. In the second part of the paper we discuse existence of solution of the obligue derivative boundary value problem for first order degeneracy elliptic system include four variates.

Key words: Generalized regular function with value in quaternions, Obligue derivative boundary value problem, Degeneracy elliptic system