A method is proposed to equate different sets of items administered to different groups of individuals using the Rasch model. A Rasch equating model was formulated to describe one common Rasch scale in different groups with different but overlapping sets of items. The item parameters can then be estimated simultaneously, avoiding different parameter estimates of common items in different groups. The model can be tested globally to test the hypothesis of one common Rasch scale, and the goodness of link can be tested. The method is based on the quasi-loglinear Rasch model. The proposed model is illustrated on real data by equating a set of 10 solid geometry items developed and administered by the Netherlands Central Institute for Test Development to 202 students in secondary education. Five tables present the model and data from the solid geometry study. (Author/SLD)