We present new developments in nonadiabatic geometric phases along two lines for systems undergoing changes of quantum state in intense fields. We first present a geometric representation of the non-Hermitian Schrodinger equation and introduce the notion of acomplexmultiphoton Aharonov-Anandan (AA) phase associated with dissipative two-level systems driven by periodic fields. The concept is further extended to include field modulation effects. We then develop the AA phase for spin-jsystems in periodic fields and find conditions for cyclic evolution for general multi-level systems. In both cases, generalizations of the Floquet formalism lead to general analytical expressions for geometric phases that can be tested by experiments.