Linkage analysis in multivariate or longitudinal context presents both statistical and computational challenges. The permutation test can be used to avoid some of the statistical challenges, but it substantially adds to the computational burden. Utilizing the distributional dependencies between π̂ (defined as the proportion of alleles at a locus that are identical by descent (IBD) for a pairs of relatives, at a given locus) and the permutation test we report a new method of efficient permutation. In summary, the distribution of π̂ for a sample of relatives at locus x is estimated as a weighted mixture of π̂ drawn from a pool of 'representative' π̂ distributions observed at other loci. This weighting scheme is then used to sample from the distribution of the permutation tests at the representative loci to obtain an empirical P-value at locus x (which is asymptotically distributed as the permutation test at loci x). This weighted mixture approach greatly reduces the number of permutation tests required for genome-wide scanning, making it suitable for use in multivariate and other computationally intensive linkage analyses. In addition, because the distribution of π̂ is a property of the genotypic data for a given sample and is independent of the phenotypic data, the weighting scheme can be applied to any phenotype (or combination of phenotypes) collected from that sample. We demonstrate the validity of this approach through simulation. The calculation of empirical P-values provides the most general solution to this problem. Currently the two most popular methods for obtaining empirical P-values for linkage analyses involve using 'gene-dropping' simulations or permutation to randomize the relationship between genotypic and phenotypic data. Both methods produce asymptotically unbiased estimates of significance (Churchill and Doerge 1994;Ott 1989). Gene-dropping requires the simulation of unlinked genotypic data that preserve the information content, allele frequency and patterns of missing data that are observed within the 'true' genotypic data. Alternatively, permutation can be used to randomize either the coefficient of genotypic sharing π, or the phenotypes, across relative pairs. Essentially, the connection between the genotypic and the phenotypic data is deliberately disrupted and the linkage analysis is repeated over a large number of permutations in order to obtain an empirical distribution of test statistics for which the null hypothesis is true. The test statistic obtained from the original, un-permuted dataset is then compared with this empirical distribution to assess significance. This approach has an attractive simplicity, but it does require that the permutations are performed across pedigrees with the same family structure by first permuting across families of the same size and then permuting within families. However, while empirical P-values offer robustness against violation of the assumptions of statistical methods (Churchill and Doerge 1994;Ott 1989), they remain computationally intensive for mult...