Spectral problems for systems of differential equations y '+A(0)y = lambdaA(1)y with lambda-polynomial boundary conditions

This paper deals with the spectral properties of boundary eigenvalue proble ms for systems of first order differential equations y' + A(0)y = lambda A( 1)y with boundary conditions which depend on the spectral parameter polynom ially. It is not assumed that Al is injective or surjective. The main resul ts concern the completeness, minimality and Riesz basis properties of the c orresponding eigenfunctions and associated functions.