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Many applications of seismology require the calculation of wave speed and attenuation in rocks saturated with multiple fluids. Squirt flow is known to be an important effect in fully saturated rocks but the extension to the multifluid case is unclear. Neglecting capillary effects, we generalize previous work on squirt flow to the case where two fluids are present. We derive expressions for the effective fluid properties, but the results depend on the spatial distributions, and not only volume fractions, of the two fluids. Our results demonstrate that such multifluid squirt flow may be responsible for hysteresis effects in elastic properties during imbibition and drainage.