In theories with a gauge-mediated mechanism of supersymmetry breaking the gravitino is likely to be the lightest superparticle and, hence, a candidate for dark matter. We show that the decay of the next-to-lightest superparticle into a gravitino can yield a non-thermal population of gravitinos which behave as a hot dark matter component. Together with the warm component, which is provided by the population of gravitinos of thermal origin, they can give rise to viable schemes of mixed dark

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... . This realization has some specific and testable features both in particle physics and astrophysics. We outline under which conditions the mechanism remains viable even when R parity is broken.