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Abstract??We study Hilbert space valued Ornstein?Uhlenbeck processes (Y(t),t? 0) which arise as weak solutions of stochastic differential equations of the typedY=JY+CdX(t) whereJgenerates aC0semigroup in the Hilbert spaceH,Cis a bounded operator and (X(t),t? 0) is anH-valued L?vy process. The associated Markov semigroup is of generalised Mehler type. We discuss an analogue of the Feller property for this semigroup and explicitly compute the action of its generator on a suitable space of twice-differentiable functions. We also compare the properties of the semigroup and its generator with respect to the mixed topology and the topology of uniform convergence on compacta. [ABSTRACT FROM AUTHOR]