Accounting for actual and anticipated developments in synchrotron radiation- and in x-ray and free electron laser techniques, we present a theory of resonant scattering of short-pulsed x rays. Both the instantaneous and integrated-over-observation-time x-ray scattering spectra are studied. Contrary to the commonly accepted notion of an instantaneous probability, we find that the correct quantity describing the resonant x-ray scattering (RXS) experiment is the probability integrated over the time of measurement. It is shown that the integral RXS probability is given by the convolution of the RXS probability for monochromatic excitation with the Wiener-Khintchine spectrum of the nonstationary incident radiation. We have found that short pulses yield a new spectral band following a non-Raman dispersion law. The finite duration of pulses results in a broadening of the Raman resonance. Some aspects of the theoretical analysis of the RXS spectra as functions of the pulse duration time are analyzed by numerical calculations.