EVER SINCE the fundamental paper of Lions and Stampacchia [IO] the subject of variational inequalities has become a very active area of study and become an important tool in the study of nonlinear partial differential equations which are subject to various types of constraints (see e.g. [l, 5, 8, 111. In [lo] the authors consider first the case of coercive forms and then, using elliptic regularization, problems involving noncoercive, but nonnegative, forms. We shall use a similar approach to study variational inequalities involving noncoercive bilinear forms and nonlinear functionals which are nice perturbations of lower semi continuous convex functionals. Furthermore, our bilinear forms need not necessarily have a finite dimensional kernel. Our investigation has been motivated by some work of Baiocchi, Gastaldi and Tomarelli (see [3, 61) where variational inequalities, involving so-called compact coercive bilinear forms, are studied. We shall introduce here a somewhat more general concept, that of a P-coercive bilinear form and study variational inequalities involving such forms and nonlinear functionals which are compact and bounded perturbations of lower semi continuous convex functionals. In the next section we shall introduce the necessary terminology, prove some preliminary results and give the statement of the abstract problem. We then shall state and prove our main abstract result and conclude the paper with applications including one to the study of a flat plate on an elastic foundation with unilateral boundary conditions (see e.g. [l] for the terminology) and one to the study of unilateral problems in semipermeable media (see [5]).