  A new type of kinetic models with non-instantaneous binary collisions is
considered. Collisions are described by a transport process in the joint state
space of a pair of particles. The interactions are of alignment type, where the
states of the particles approach each other. For two spatially homogeneous
models with deterministic or stochastic collision times existence and
uniqueness of solutions, the long time behavior, and the instantaneous limit
are considered, where the latter leads to standard kinetic models of Boltzmann
type.
