There appear to be two different kinds of theoretical results about stochastic patch-occupancy metapopulation models: those recently proposed by Gyllenberg and Silvestrov (1994) about metapopulations including a very stable patch, and those by Darroch and Seneta (1965) about more general metapopulations. Based on the spectral theory of linear operators, it is shown that the results by Gyllenberg and Silvestrov (1994) are a limiting case of those by Darroch and Seneta (1965). Taking the examples proposed by Gyllenberg and Silvestrov (1994) as a case study, the application and relevance of these results are discussed, with a particular stress to their bearing on real metapopulations.