We shall establish sufficient conditions for the existence of at least one nonoscillatory solution and for oscillation of all solution of the following system of differential equations \[ u'_i=|u_{3-i}|^{ambda_i}peratorname{sgn}u_{3-i}+(-1)^{i-1}b_i(t)u_i\quad(i=1,2),\quadambda_1ambda_2eq1. \]