This paper discusses the computation of multiplek-statistics and provides techniques for seminvariantk… through weight 8. After a review of pertinent background material, specific techniques for calculation through weight 4 are presented for desk calculation with application to moment formulae involving the mean and variance. Then the various methods of calculating seminvariantk… through weight 8 are examined, Basic formulae needed for the recommended methods are presented in tabular form. The general problem, of moments and estimates of moments ofk-statistics is then treated. A machine program is available through weight 8. Specific references are given throughout so the reader who is unfamiliar with this material may examine earlier results.