  A short-time dynamic approach to weak first order phase transitions is
proposed. Taking the 2-dimensional Potts models as examples, from short-time
behaviour of non-equilibrium relaxational processes starting from high
temperature and zero temperature states,x pseudo critical points K^{*} and
K^{**} are determined. A clear difference of the values for K^{*} and K^{**}
distinguishes a weak first order transition from a second order one. At the
pseudo critical points, pseudo critical exponents can be estimated.
