Recently, Arecchi, Bern\'e, and Sona reported results of theoretical and experimental investigations on the twofold joint photocount distributions of a stationary Gaussian-Markovian radiation field. In this paper, we generalize their results by deriving the
N-fold joint photocount distribution of a Gaussian (thermal) radiation field of arbitrary spectral profile, when the counting-time intervals are short compared to the coherence time of the light. The present analysis provides simple recurrence relations for the
N-fold joint photocount distributions and for their generalized factorial moments. These relations are derived with the help of an $N\ifmmode\times\else\texttimes\fi{}N$ generating matrix which is introduced here. The present analysis also indicates to what extent the
N-fold joint photocount distributions contain useful information about the higher-order coherence properties of the radiation field.