The guiding-center equations are derived for electrons in arbitrarily
intense laser fields also subject to external fields and ponderomotive
forces. Exhibiting the relativistic mass increase of the oscillating
electrons, a simple frame-invariant equation is shown to govern the be
havior of the electrons for sufficiently weak background fields and po
nderomotive forces. The parameter regime for which such a formulation
is valid is made precise, and some predictions of the equation are che
cked by numerical simulation.