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In this paper, we discuss the generalized Marshall–Olkin Bivariate Exponential Distribution. This model was briefly mentioned in Marshall and Olkin (1967b) and Esary and Marshall (1974) but, to our knowledge, has not been studied further in the literature. This model extends the classical three-parameter Marshall–Olkin bivariate exponential (MOBVE) distribution by allowing the common shock to affect the two variables asymmetrically. As a result, the generalized model is tie-free almost surely, in contrast to the MOBVE model, which assigns positive probability to ties (X = Y). The only exception occurs when two of its parameters are equal, in which case the model reduces to the classical MOBVE distribution. (...) Finally, we present two real data analyses, one having ties between the two variables and the other having no ties.