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Let X be a Markov process, which is assumed to be associated with a (non-symmetric) Dirichlet form (ε ,D(ε )) on L2 (E;m) . For u ∈D(ε)ε ,the extended Dirichlet space, we give necessary and sufficient conditions for the Girsanov transform to induce a positive supermartingale and hence to determine the Girsanov transformed process Y of X.Morever we present a sufficient condition under which Y is associated with a semi-Dirichlet form and give an explicit representation of the semi-Dirichlet.