Experimental designs for complete diallel cross(CDC) system IV with equal number of replications of each cross has been studied extensively in the literature. In this book, we have proposed incomplete block designs for CDC system IV with unequal number of replications for crosses through two-associate classes of partially balanced incomplete block (PBIB (2))designs where none of two treatments which are ith associates occur together exactly in the same blocks (i =1 ,2) is zero. In addition to the block effects and general combining abilities effects, the model also includes the parameter of specific combining abilities effects. The procedure of analyses of these designs has also been developed. The analysis includes the analysis of variance and the estimation (intra-block, inter-block and combined) of general and specific combining abilities. Tests of certain hypotheses concerning some general parameters are also given. The efficiency (optimality) of the proposed designs is also considered in comparison to RCBD. The method of analysis (intra-block, inter-block and combined) has been illustrated with the help of numerical data.