The north-American marine gastropod Crepidula fornicata (Linné 1758), commonly called slipper limpet, has been introduced accidentally in Great Britain, along with American oysters (Crassostrea virginica) at the end of the 19th century. Its spreading, enhanced by oyster transport and international shipping, turned into invasion of a lot of benthic grounds along the North-European coasts. When local conditions are favorable to larval confinement and adult growth, the invasion by very dense populations may deeply change initially sandy or muddy benthic communities into similar “slipper limpet communities”. Competition for space eliminates several species of native infauna, and hampers the survival of some epibenthic bivalves such as the scallop Pecten maximus. As the clogging of dredges by superabundant slipper limpets drastically limits scallop fishing, some insight in the future distribution and abundance of both species (Crepidula and Pecten) seems necessary, especially in the English Channel where the scallop is intensively harvested. An original model, storing in a “intraspecific matching matrix” the numbers of pairs of aged animals present in the slipper limpet chains, has been developed to take into account the year-class association and stack formation specific to Crepidula fornicata. Then, an “interspecific matching matrix” component has been added to that “intraspecific matching matrix” in order to describe the simple year-class structure of the scallop along with the age distribution of slipper limpets stuck on scallop shells and forming the base of chains. Such a model can explore the dynamics of both populations at a secular time scale. This first part of work details the 0D-behavior of the populations, alone or together, on 1 m2 benthic area. As far as the scallop is concerned, the fact that class 1 cannot recruit in dense populations until the death of old animals has freed some place induces a limit-cycle, with a 11 years period, and a large amplitude. On the contrary, in the case of the slipper limpet, because of the constant possibility for class 1 to recruit on the top of existing colonies, even if the bottom coverage is total, the population reaches a stable steady state abundance, without significant oscillations. Competition for space between the two species does not alter significantly the slipper limpet, whereas it lowers the mean abundance and alters (by damping and slowing down) the limit cycle of the scallop.