We study generalized Mehler semigroups, introduced in [7], with special emp
hasis on the non-Gaussian case. We review and simplify the method of constr
uction. In the general (non-Gaussian) case we construct an associated cadla
g Markov process in an appropriate state space obtained as a solution of a
stochastic equation which can be solved 'omega by omega'. We also show tigh
tness of the associated (r, p)-capacities. Invariant measures, time regular
ity and a definition of the generator are also studied.