A nonlinear elliptic system involving the p-Laplacian is considered in the whole RN: Existence of nontrivial solutions is obtained by applying critical point theory; also a regularity result is established.A nonlinear elliptic system involving the p-Laplacian is considered in the whole RN . Existence of nontrivial solutions is obtained by applying critical point the ory; also a regularity result is established. 2000 Mathematics Sub ject Classification: 35J70, 35B45, 35B65