The projection of 6 motoneurons to a flat sheet of muscle fibers, the superficial flexor muscle of the crayfish Procambarus clarkii, was examined. Each of the motoneurons was individually identifiable. Each muscle fiber could be homologized with good accuracy, in successive preparations. Intracellular recording was carried out while stimulating single axons at 10 Hz. When each animal was examined, the junction potentials (JP) produced by any given axon in neighboring muscle fibers were of very dissimilar sizes, bordering on a random sequence. When homologous muscle fibers were examined in a series of animals, the JP received by these fibers were also very dissimilar. Population averages showed that the minimum and maximum probabilities of innervation for each axon occurred at the edges of the muscle sheet; between the minimum and maximum values, the probability of innervation increased linearly as a function of position in the muscle; and size of the JP produced by each axon was a roughly linear function of position across the muscle. There may be a process controlling development of synapses, such that the strength of a synapse on any given fiber is not determined but is probabilistically controlled, i.e., a random process. A single gradient across the muscle probably controls the parameters of this random process. For any given axon mean synapse strength increases or decreases continuously from one end of the muscle to the other. There is no recognition between axon and muscle fiber. The probability that a fiber is innervated by an axon is simply the probability that the axon sends out at least 1 ending in its region.