Summary: Our main purpose is to establish the existence of entire explosive positive radial solutions of the quasilinear elliptic system
where , . The main results of the present paper are new and extend the previously known results [see, for example, A. V. Lair and A. W. Wood, J. Differ. Equations 164, No. 2, 380–394 (2000; Zbl 0962.35052)].