We show that {\it strong} anomalous diffusion, i.e. \mean{|x(t)|^q} \sim
t^{q \nu(q)} where qν(q) is a nonlinear function of q, is a generic
phenomenon within a class of generalized continuous-time random walks. For such
class of systems it is possible to compute analytically nu(2n) where n is an
integer number. The presence of strong anomalous diffusion implies that the
data collapse of the probability density function P(x,t)=t^{-nu}F(x/t^nu)
cannot hold, a part (sometimes) in the limit of very small x/t^\nu, now
nu=lim_{q to 0} nu(q). Moreover the comparison with previous numerical results
shows that the shape of F(x/t^nu) is not universal, i.e., one can have systems
with the same nu but different F.Comment: Final versio
