  We investigate particular cosmological models, based either on tachyon fields
or on perfect fluids, for which soft future singularities arise in a natural
way. Our main result is the description of a smooth crossing of the soft
singularity in models with an anti-Chaplygin gas or with a particular tachyon
field in the presence of dust. Such a crossing is made possible by certain
transformations of matter properties. Some of these cosmological evolutions
involving tachyons are compatible with SNIa data. We compute numerically their
dynamics involving a first soft singularity crossing, a turning point and a
second soft singulatity crossing during recollapse, ending in a Big Crunch
singularity.
