Finney and Outhwaite [2] introduced serially balanced sequences into the statistical literature. They classified these sequences into two types, viz., type I and type II. Sampford [3] gave many methods of construction and analysis of these sequences. But these authors were concerned only with sequences balanced for a single residual. We shall deal with sequences balanced for pairs of residual effects. Two important methods of construction of these sequences are given. One is from designs balanced for residuals within blocks and the other from “round table solutions.” The analysis of the sequence is given with a numerical example. The appendix contains the plans of five sequences for four to eight treatments. Experimenters who are interested in the practical application of these sequences need go only through parts 1 and 4, conclusion and the appendix. For, part 1 explains where the sequences are to be used, part 4 gives the analysis of these sequences and explains its limitations, the conclusion points out a minor advantage of the SSBS over the SBS, and the appendix contains the plans of some sequences.