We give a general model of partially asynchronous, distributed load-balancing algorithms for the discrete load model in parallel computers, where the processor loads are treated as non-negative integers. We prove that all load-balancing algorithms in this model are finite. This means that all load-balancing algorithms based on this model are guaranteed to reach a stable situation at a certain time (which depends on the particular algorithm) at which no load will be sent from one processor to another. With an additional assumption, we prove that the largest load difference between any two processors, in the final stable situation of the load-balancing algorithms in this model, is upper-bounded by the diameter of the topology. © 2007 Springer.