The work is devoted to the systematic study of periodic and chaotic forced oscillations. Recently, on the basis of method of complete bifurcation groups new nonlinear effects were found in driven damped systems with various nonlinearities of elastic restoring forces. Construction of complete bifurcation groups is based on the method of stable and unstable periodic regimes continuation on parameter. Aim of the work – to study new nonlinear effects induced by varying linear dissipation in following dynamical systems with typical nonlinear restoring forces: symmetric trilinear and quadratic, bilinear, cubic with asymmetry, Duffing, pendulum. The work presents new qualitative and quantitative results of nonlinear dynamics in the systems with increasing linear dissipation.