  We propose two new classes of time integrators for stiff DEs: the
implicit-explicit exponential (IMEXP) and the hybrid exponential methods. In
contrast to the existing exponential schemes, the new methods offer significant
computational advantages when used with preconditioners. Any preconditioner can
be used with any of these new schemes. This leads to a broader applicability of
exponential methods. The proof of stability and convergence of these
integrators and numerical demonstration of their efficiency are presented.
