  We present numerical investigations of the short-time dynamics at criticality
in the 1D Potts model with power-law decaying interactions of the form
1/r^{1+sigma}. The scaling properties of the magnetization, autocorrelation
function and time correlations of the magnetization are studied. The dynamical
critical exponents theta' and z are derived in the cases q=2 and q=3 for
several values of the parameter $\sigma$ belonging to the nontrivial critical
regime.
