The Widom-Rowlinson model of a fluid mixture is studied using a new cl
uster algorithm that is an adaptation of the invaded cluster method pr
eviously applied to Potts models. The algorithm overcomes the difficul
ties of treating continuum hard-core systems and has almost no critica
l slowing down. Our estimates of beta/nu and gamma/nu for the two-comp
onent fluid are consistent with the Ising universality class in two an
d three dimensions. We also present preliminary results for the three-
component fluid.