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This paper is concerned with the framework of frequent episode discovery in event sequences. A new temporal pattern, called the generalized episode, is defined, which extends this framework by incorporating event duration constraints explicitly into the pattern's definition. This new formalism facilitates extension of the technique of episodes discovery to applications where data appears as a sequence of events that persist for different durations (rather than being instantaneous). We present efficient algorithms for episode discovery in this new framework. Through extensive simulations, we show the expressive power of the new formalism. We also show how the duration constraint possibilities can be used as a design choice to properly focus the episode discovery process. Finally, we briefly discuss some interesting results obtained on data from manufacturing plants of General Motors.