[en] The complex time-dependent solutions of the first order in deltasub(t) (nonrelativistic) and second order (relativistic) nonlinear local or nonlocal equations have the conserving normalization (nonrelativistic case) or charge (relativistic case). These conservation laws stipulate the nonvalidity (in general) of the Hobbart-Derrick theorem and a possibility of having stable soliton solutions to these nonlinear equations if the nonlinear interactions obey certain conditions. These conditions are formulated for relativistic and nonrelativistic equations with both local and nonlocal interactions and for systems of the relativistic equations. In the relativistic case there exist two critical values of the frequency, ωsub(b) and ωsub(c), such that the solitons are stable for small or finite perturbations if ω>ωsub(b) and ω>ωsub(c) respectively. The values of ωsub(b) and ωsub(c), explicitly calculated for the cubic plus fifth power nonlinearity, are in agreement with the results of numerical solution