We study the properties of optical fields created by interfering polychromatic stationary waves that have different spectra and polarizations. Such fields can exhibit both deterministic and random intensity and polarization beatings, where the latter stands for a periodic variation of the field polarization state. For visible light, the beating period enters the femtosecond scale already when the central wavelengths of the waves differ by 10 nm. If the bandwidth of at least one of the waves is also on the order of 10 nm, the periodic variations are accompanied by ultrafast random changes which cannot be measured directly. We propose a set of statistical characteristics for such rapidly varying vector fields and practical methods to determine them in terms of fully time-averaged quantities. Our results may have impact on a variety of fundamental and applied aspects of optical polarimetry and interferometry.