A model for the retino-tectal projection is proposed which assumes that axonal growth proceeds predominantly in the direction of maximal slope of a guiding substance (or, more generally, of a system parameter subsuming the effect of several substances). The spatial distribution of this parameter, in turn, results from the interaction of components of retinal axons (which are graded with respect to position of origin in the retina) and tectal components. One or two gradients in each dimension of retina and tectum suffice. Conditions for the generation of a reliable projection on this basis are relatively simple and consistent with conventional enzyme and receptor kinetics. Adhesive forces could but need not be involed in the guiding mechanism. The slope of guiding substances that interfere with an intracellular pattern-forming mechanism within the growth cone may determine the polarity of activation and thus the direction of growth. Generation of primary projections and some features of regulation such as independence of projections on neural pathways, and observations on the innervation of rotated pieces of tectum, can be explained on the basis of the model. The model can be extended by introducing additional production of guiding substance depending on the density, and duration of presence, of fibre terminals in the course of innervation. This simple mechanism would suffice for observed effects of compression and expansion of the map following ablation of retinal and tectal tissue, respectively. It may but need not be involved in the primary projection, too.