The influence of an external field acting differently on the twoconstituents of a binary colloidal mixture performing Browniandynamics is investigated by computer simulations and a simpletheory. In our model, half of the particles(A particles) are pulled by an external force F⃗(A)while the other half (B particles) are pulled by anexternal force F⃗(B). If F⃗(A) andF⃗(B) are parallel and the field-free state is amixed fluid, previous simulations (Dzubiella J et al 2002 Phys. Rev. E 65 021402) have shown a nonequilibriumpattern formation involving lanes of A or B particles only,which are sliding against each other in the direction of theexternal forces. In this paper, we generalize the situation bothto nonparallel external forces and to field-free crystallinestates. For nonparallel forces, lane formation is also observedbut with an orientation tilted with respect to theexternal forces. If the field-free state is crystalline, acontinuous increase of the parallel external forces yields anovel re-entrant freezing behaviour: the crystal firstmelts mechanically via the external force and thenrecrystallizes into demixed crystalline lanes sliding againsteach other.