In this paper, we consider the Cauchy problem for the equation of dislocation of crystals utt&2u+u=u2+u3. The necessary and sufficient conditions of the existence of global solutions are obtained for E(0)=12 (&u1&2 L2+&u0&2 H1) & Rn u of (s) ds dx<d (f(s)=s2+s3, d is a given constant). We give the estimation of life span for the nonglobal solution. The existence and the nonexistence of solutions for E(0)=d are also considered. 1998 Academic Press