We have used the Fermilab 30-in. bubble-chamber-hybrid spectrometer to study neutral-strange-particle production in the interactions of 200-GeV/c protons and + and K+ mesons with nuclei of gold, silver, and magnesium. Average multiplicities and inclusive cross sections for K0 and are measured, and a power law is found to give a good description of their A dependence. The exponent characterizing the A dependence is consistent with being the same for K0 and production, and also the same for proton and + beams. Average K0 and multiplicities, as well as their ratio, have been measured as functions of the numbers of projectile collisions p and secondary collisions s in the nucleus, and indicate that rescattering contributes significantly to enhancement of production but not to K0 production. The properties of events with multiple K0's or also corroborate this conclusion. K0 rapidities are in the central region and decrease gently with increasing p, while rapidities are in the target-fragmentation region and are independent of p. K0 and multiplicities increase with the rapidity loss of the projectile, but their rapidities do not.