An effective action technique for the time evolution of a closed system consisting of one or more mean fields interacting with their quantum fluctuations is presented. By marrying large N expansion methods to the Schwinger-Keldysh closed time path (CTP) formulation of the quantum effective action, causality of the resulting equations of motion is ensured and a systematic, energy conserving and gauge invariant expansion about the quasi-classical mean field(s) in powers of 1/N developed. The

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... al method is exposed in two specific examples, O(N) symmetric scalar ł^4 theory and Quantum Electrodynamics (QED) with N fermion fields. The ł^4 case is well suited to the numerical study of the real time dynamics of phase transitions characterized by a scalar order parameter. In QED the technique may be used to study the quantum non-equilibrium effects of pair creation in strong electric fields and the scattering and transport processes in a relativistic e^+e^- plasma. A simple renormalization scheme that makes practical the numerical solution of the equations of motion of these and other field theories is described.