  We introduce a new framework of highly-anisotropic hydrodynamics that
includes dissipation effects. Dissipation is defined by the form of the entropy
source that depends on the pressure anisotropy and vanishes for the isotropic
fluid. With a simple ansatz for the entropy source obeying general physical
requirements, we are led to a non-linear equation describing the time evolution
of the anisotropy in purely-longitudinal boost-invariant systems. Matter that
is initially highly anisotropic approaches naturally the regime of the perfect
fluid. Thus, the resulting evolution agrees with the expectations about the
behavior of matter produced at the early stages of relativistic heavy-ion
collisions. The equilibration is identified with the processes of entropy
production.
