In this article we study quasilinear multipower systems of two equations of two types, in a domain Ω of R^{N} : with absorption terms, or mixed terms. Despite of the lack of comparison principle, we prove a priori estimates of Keller-Osserman type. Concerning the mixed system , we show that one of the solutions always satisfies Harnack inequality. In the case Ω=B(0,1)\{0}, we also study the behaviour near 0 of the solutions of more general weighted systems, giving a priori estimates and removability results. Finally we prove the sharpness of the results.