When a thermodynamic process happens in such a way that the system remains infinitesimally close to an equilibrium state at all times.
This process happens so slowly and in very small steps that properties in one part of the system do not change any faster than those in other parts.
An exact opposite of a quasi-equilibrium process is for example sudden contraction or sudden expansion of gas in a piston-cylinder arrangement.
Quasi-equilibrium processes are ideal processes. But many actual processes can be approximated as quasi-equilibrium processes.