Consider ( M , g ) as an m-dimensional compact connected Riemannian manifold without boundary. In this paper, we investigate the first eigenvalue λ 1 , p , q of the ( p , q ) -Laplacian system on M. Also, in the case of p,q>n we will show that for arbitrary large λ 1 , p , q there exists a Riemannian metric of volume one conformal to the standard metric of S m .