Nonregular factorial designs are getting more attention due to its run size economy and flexibility of accommodating various combinations of factors with different numbers of levels. However, resolution and MA cannot assess, compare and rank nonregular factorial designs systematically. The concepts of minimum moment aberration proposed by Xu and Lau (2004) and Xu (2005) for blocked regular designs and moment aberration pro jection proposed by Xu and Deng (2005) for unblocked nonregular designs are extended to blocked nonregular designs. New optimality criteria are proposed for ranking blocked nonregular designs. Optimal blocked nonregular designs for 12 runs, 16 runs and 20 runs with two levels and for 18 runs and 27 runs with three levels are given.