A discrete time process, with law µ, is quasi-exchangeable if for any finite permutation σ of time indices, the law µ σ of the resulting process is equivalent to µ. For a quasi-exchangeable stationary process, our main results are (1) if the process is ergodic then it is isomorphic to a Bernoulli process and (2) if the family of all Radon-Nikodym derivatives {dµ^σ/dµ} is uniformly integrable then the process is a mixture of Bernoulli processes, which generalizes De Finetti's Theorem. We give application of (1) to some determinantal processes.