We present an approach for describing the properties of a quasi-monoch
romatic, beam-like field that is both partially polarized and partiall
y coherent from the spatial standpoint. It is based on the use of a si
ngle 2 x 2 matrix, called the beam coherence-polarization matrix, whos
e elements have the form of mutual intensities. This approach, which c
an be viewed as an approximate form of Wolf's general tensorial theory
of coherence, appears to be very simple, yet it is able to cover sign
ificant aspects of the beam behaviour that would not be accounted for
by a scalar theory or by a local polarization matrix approach. A pecul
iar interference law applying to mutual intensities is derived. We sho
w through simple examples how this approach leads to distinguish field
s that would appear identical in a scalar treatment or in a local pola
rization matrix description. Hints for extensions are given.