We provide a covariant and gauge-invariant approach to the question ofhow a first-order pressure can be incorporated self-consistently in acosmological scenario. The approximation is relevant, in the linearregime, to weakly self-interacting or warm dark matter models. We alsoderive number density fluctuations in which new modes appear becausethe number density fluctuations are no longer simply proportional to thedensity fluctuations.