Methods of nonequilibrium quantum statistical mechanics are applied to the problem of estimating effects arising from the finite lifetime of the core hole in soft X-ray emission spectra. A comparison is made with the formalism for absorption spectra where equilibrium methods are appropriate. A diagrammatic method for estimating lifetime effects is described. It is shown how the validity of the Weisskopf and Wigner approximation is related to two basic assumptions on the decay of the core hole, namely the absence of memory effects and exponential decay of the core hole. Possible memory effects are discussed in detail using a solvable model, and their effect on the spectrum when present is indicated. In particular it is shown that in the model the recoil energy associated with an initial electron bombardment exciting the core, even if appreciable in magnitude, cannot be expected to give rise to a width of the core level, thus broadening the spectrum.