  We consider systems of semilinear wave equations in three space dimensions
with quadratic nonlinear terms not satisfying the null condition. We prove
small data global existence of the classical solution under a new structural
condition related to the weak null condition. For two-component systems
satisfying this condition, we also observe a new kind of asymptotic behavior:
Only one component is dissipated and the other one behaves like a free solution
in the large time.
