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The gravitational evolution of scale free initial spectra $P(k)\propto k^n$in an Einstein-de Sitter universe is widely believed to be self-similar for$-3<n<4$. However, for $-3<n<-1$ the existence of self-similar scaling has notbeen adequately demonstrated. Here we investigate the possible breaking ofself-similar scaling due to the nonlinear contributions of long wave modes. For$n<-1$ the nonlinear terms in the Fourier space fluid equations contain termsthat diverge due to contributions from wavenumber $k\to 0$ (the long wavelimit). To assess the possible dynamical effects of this divergence the limitof long wave contributions is investigated in detail using two differentanalytical approaches.  Perturbative contributions to the power spectrum are examined. It is shownthat for $n<-1$ there are divergent contributions at all orders. However, atevery order the leading order divergent terms cancel out exactly. This does notrule out the existence of a weaker but nevertheless divergent net contribution.The second approach consists of a non-perturbative approximation, developed tostudy the nonlinear effects of long wave mode coupling. A solution for thephase shift of the Fourier space density is obtained which is divergent for$n<-1$. A kinematical interpretation of the divergence of the phase shift,related to the translational motion induced by the large-scale bulk velocity,is given. Our analysis indicates that the amplitude of the density is {\it not}affected by the divergent terms. Thus both analytical approaches lead to theconclusion that the self-similar scaling of physically relevant measures of thegrowth of density perturbations is preserved.Comment: 26 pages, uuencoded compressed postscript file, no figures. Submitted  to Ap

Self-similar Evolution of Gravitational Clustering: Is N = -1 Special?