  We present a simple nonlinear relaxation equation which contains the Debye
equation as a particular case. The suggested relaxation equation results in
power-law decay of fluctuations. This equation contains a parameter defining
the frequency dependence of the dielectric permittivity similarly to the
well-known one-parameter phenomenological equations of Cole-Cole, Davidson-Cole
and Kohlrausch-Williams-Watts. Unlike these models, the obtained dielectric
permittivity (i) obeys to the Kramers-Kronig relation; (ii) has proper
behaviour at large frequency; (iii) its imaginary part, conductivity, shows a
power-law frequency dependence \sigma ~ \omega^n where n<1 corresponds to
empirical Jonscher's universal relaxation law while n>1 is also observed in
several experiments. The nonlinear equation proposed may be useful in various
fields of relaxation theory.
