summary:We study asymptotic and oscillatory properties of solutions to the third order differential equation with a damping term x′′′(t)+q(t)x′(t)+r(t)∣x∣λ(t)sgnx(t)=0,t≥0. We give conditions under which every solution of the equation above is either oscillatory or tends to zero. In case λ≤1 and if the corresponding second order differential equation h′′+q(t)h=0 is oscillatory, we also study Kneser solutions vanishing at infinity and the existence of oscillatory solutions