We consider the Dirichlet problem for the quasilinear elliptic system -divσ(x,u(x),Du(x))=f on Ω
u(x)=0 on \partialΩ for a function u:Ω→R^m, where Ω is a bounded open domain in Rⁿ. For arbitrary right hand side f∈ W^-1,p'(Ω) we prove existence of a weak solution under classical regularity, growth and coercivity conditions, but with only very mild monotonicity assumptions.