  The well known scaling laws relating critical exponents in a second order
phase transition have been generalized to the case of an arbitrarily higher
order phase transition. In a higher order transition, such as one suggested for
the superconducting transition in Ba$_{0.6}$K$_{0.4}$BiO$_3$ and in
Bi$_2$Sr$_2$CaCu$_2$O$_8$, there are singularities in higher order derivatives
of the free energy. A relation between exponents of different observables has
been found, regardless of whether the exponents are classical (mean-field
theory, no fluctuations, integer order of a transition) or not (fluctuation
effects included). We also comment on the phase transition in a thin film.
