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We obtain a criterion for the quasi-regularity of generalized (non-sectorial)Dirichlet forms, which extends the result of P.J. Fitzsimmons on thequasi-regularity of (sectorial) semi-Dirichlet forms. Given the right (Markov)process associated to a semi-Dirichlet form, we present sufficient conditionsfor a second right process to be a standard one, having the same state space.The above mentioned quasi-regularity criterion is then an application. Theconditions are expressed in terms of the associated capacities, nests ofcompacts, polar sets, and quasi-continuity. A second application is on thequasi-regularity of the generalized Dirichlet forms obtained by perturbing asemi-Dirichlet form with kernels .

On the quasi-regularity of non-sectorial Dirichlet forms by processes having the same polar sets