This paper is concerned with tests based on sample spacings for the two sample problem with nuisance location and scale parameters--Part A--Sections 1 through 4, and for the goodness of fit problem with nuisance scale and location parameters, Part B, Sections 5 through 7. Estimation of the nuisance scale parameter is also considered. The notation and methods of proof, as well as the basic results of the preceding paper, Blumenthal (1966) are used without restatement. That paper is referred to as Spacings I, throughout the sequel.