Infinite population genetic models with general type space incorporating mu
tation, selection and recombination are considered. The Fleming-Viot measur
e-valued diffusion is represented in terms of a countably infinite-dimensio
nal process. The complete genealogy of the population at each time can be r
ecovered from the model. Results are given concerning the existence of stat
ionary distributions and ergodicity and absolute continuity of the stationa
ry distribution for a model vith selection with respect to the stationary d
istribution for the corresponding neutral model.