SUMMARY: Noninformative priors are developed, using the reference prior approach, for multipara-meter problems in which there may be parameters of interest and nuisance parameters. For a given grouping of parameters and ordering of the groups, intuitively, according to inferential importance, an algorithm for determining the associated reference prior is presented. The algorithm is illustrated on the multinomial problem, with discussion of the variety and success of various groupings and ordering strategies. © 1992 Biometrika Trust.