We postulate that positional information for secondary embryonic fields is generated by a cooperative interaction between two pairs of differently determined cell types. Positional information is thus generated at the boundaries between cells of different determination. The latter are assumed to result from the primary pattern formation in the embryo. The application of this model to vertebrate limbs accounts for the pairwise determination of limbs at a particular location, with a particular handedness and alignment to the main body axes of the embryo. It accounts further for the gross difference in the regeneration of double anterior and double posterior amphibian limbs as well as for the formation of supernumerary limbs after certain graft experiments including supernumeraries in which the dorsoventral polarity changes or which consist of two anterior or two posterior halves. Our model provides a feasible molecular basis for the polar coordinate model and successfully handles recently found violations, for instance formation of supernumerary limbs after ipsilateral grafting with 90 degrees rotation. The most frequent types of developmental malformations become explicable. The models allow specific predictions which are fully supported by recent experiments (see the accompanying paper of M. Maden).