A theory of projections in the nervous system (such as the retino-tectal projection) is proposed. Components of axonal growth cones and target tissue interact and cooperate, within the area of contact, to generate a guiding parameter, in the simplest case a "guiding substance" of distribution p. The components which are involved in this production are assumed to have graded distributions with respect to position in the projecting and target area, respectively. The distribution p thus produced guides the growth cone in the direction of maximal slope until the minimal value of p is reached. In this way, each growth cone can be guided to a position on the target tissue which depends on the origin of the fiber in such a manner that a projection results. Adhesive forces could but need not be involved in the guiding mechanism. The slope of p may interfere with an intracellular pattern forming mechanism within the growth cone, determining the polarity of activation (as modelled previously on the basis of autocatalysis and lateral inhibition) and thus the direction of growth. For the generation of a distribution of p leading to a reliable projection, simple graded distributions in the projecting and target area suffice, involving one or two components in each dimension. Their effect on the generation of p may be activatory as well as inhibitory. Exponential gradients give rise to particularly simple mapping functions. The following is an example of this general type of model: Growth cones as well as target tissue contribute to the production of a guiding substance. For each dimension, there is, in the target tissue, an exponentially graded component exerting (directly or indirectly) two functions: it actively produces guiding substance p and it interacts, in an inhibitory fashion, with the production of p by a component of the growth cone (which is, in turn, graded with respect to position of origin in the projecting area). While the theory is proposed as a fair approximation of the primary events in neural projections, superimposed regulatory effects can also be incorporated. These include fiber-fiber interactions, mechanisms smoothing out unequal density distributions of axon terminals and effects of time of arrival of fibers on the projection, which have been proposed previously as primary mechanisms generating projections. A further extension of the model is to assume that crude and more refined positional specificity is determined in a combinatorial fashion, allowing the possibility of interchanges and transformations of parameters.