The development of fractional replicate plans which consist of irregular fractions of factorial experiments is presented. The method of constructing irregular fraction plans is developed for the general snfactorial experiment. However, the plans which are found to be of greatest practical value are plans for the 3/2mreplicate of the 2nexperiment. Although these plans introduce correlations between some of the estimates, the correlations do not affect individual tests on the parameters. Some irregular fraction plans permit the estimation of main effects and two-factor interactions with fewer trials than is required with an orthogonal plan. A straightforward procedure for obtaining estimates of the main effects and “important” interactions and estimates of their variances, covariances and correlation coefficients is presented for the 3/2mreplicate plans.