The manner in which a pumping wave of high amplitude can produce parametric instabilities in a plasma is investigated. A very simple derivation of the nonlinear polarizabilities is given for the case when the pumping wave is homogeneous. From this nonlinear polarizability, a derivation of the accurate nonlinear dispersion relation is given. One finds unstable waves by solving this nonlinear dispersion relation. The critical level of the pumping wave is very much reduced if the proper modes allow carrying out the stimulated Brillouin effect. A pumping wave with a cyclotron resonance gives a particularly low critical level.