An approximation to the existing optimal algorithm for simultaneously tracking several moving targets is proposed which greatly reduces the required memory and number of calculations, but nevertheless retains reasonable accuracy (as is shown by analytic consideration and by Monte Carlo simulations) when the number of states is much greater than the number of targets. It is shown where errors arise in the approximation and how the errors tend to stabilize as the process evolves. Computational results on a highly idealized biological population surveillance problem are given that tend to confirm assertions concerning the relative computational efficiency and accuracy of the suboptimal rule in comparison to the optimal solution. A more realistic radar simulation study (20 targets and 10 000 states) is reported that suggests the scope of application of thc methodology proposed here.