Does a light beam of very narrow bandwidth always behave as a monochromatic beam?

We show by analyzing coherence and polarization properties of narrow-band stochastic electromagnetic beams that a light beam of a very narrow bandwidth does not necessarily behave as a monochromatic beam with regards to its coherence and polarization properties. Our analysis also provides a new insight into the relation between the theories of coherence and polarization in the space–time domain and in the space-frequency domain.