  In this paper, we study the driven-dissipative p-spin models for $p\geq 2$.
In thermodynamics limit, the equation of motion is derived by using a
semiclassical approach. The long-time asymptotic states are obtained
analytically, which exhibit multi-stability in some regions of the parameter
space. The steady state is unique as the number of spins is finite. But the
thermodynamic limit of the steady-state magnetization displays nonanalytic
behavior somewhere inside the semiclassical multi-stable region. We find both
the first-order and continuous dissipative phase transitions. As the number of
spins increases, both the Liouvillian gap and magnetization variance vanish
according to a power law at the continuous transition. At the first-order
transition, the gap vanishes exponentially accompanied by a jump of
magnetization in thermodynamic limit. The properties of transitions depend on
the symmetry and semiclassical multistability, being qualitatively different
among $p=2$, odd $p$ ($p\geq 3$) and even $p$ ($p\geq 4$).
