Bohm sheath criteria and double layers are investigated in general multispecies plasmas containing a number of lighter, thermal species, described by Boltzmann distributions, in the presence of a number of heavier species described by cold fluid theory. A nonlinear description for one-dimensional stationary self-similar electrostatic modes is given using the Sagdeev potential. We generalize the classic Bohm sheath criteria by giving appropriate multispecies definitions of drift and ion-acoustic velocities, leading to a global supersonic condition. We also discuss plasmas with only one Boltzmann species, to show that double layers cannot be supported at all, no matter how many cold fluid species are present, and do so by analytical rather than numerical means, based on the full Sagdeev potential. Series expansions for weak double layers occurring in the literature can only claim to find double layers, erroneously as we indicate, by not confirming whether the necessary consistency relations are obeyed, and also by not checking that ‘neglected’ terms in the expansion overwhelm those retained.