We consider parametric equations driven by the sum of a p-Laplacian and a Laplace operator ( the so-called ( p, 2)-equations). We study the existence and multiplicity of solutions when the parameter lambda > 0 is near the principal eigenvalue lambda(1)(p) > 0 of ( -Delta(p),w(0)(1)p(Omega)). We prove multiplicity results with precise sign information when the near resonance occurs from above and from below of lambda(1()p) > 0.