This paper establishes two theorems on the stability of a semi-affine variational inequality problem and gives a characterization of the stability of the generalized linear complementarity problem when the defining matrix is copositive plus on the constraint cone. One of our results gives an affirmative answer to the second open problem stated by M. S. Gowda and T. S. Seidman in their paper ''Generalized linear complementarity problems" (Math. Programming Vol. 46, 1990, 329–340).