The theory of microdosimetry is extended to include particulate and non- uniformly distributed sources typical of internally deposited radioisotopes. An example is presented in which stationary particulates of 239Pu of negligible physical size are distributed at random in a tissue in which the sensitive sites are also assumed to be randomly distributed. Preliminary calculations are reported for this model of the probability density in specific energy of all the sites and of the fraction of sites in which no energy is deposited for particulates that emit between 1 and 100,000 alpha particles. (auth)