The relationship between the class of Latin, Graeco-Latin and Hyper-Graeco-Latin squares which can be formally classified as orthogonal fractional replicate plans and the totality of Latin, Graeco-Latin and Hyper-Graeco-Latin squares is discussed. AvXvsquare for which thetletters of the alphabet that represents the treatments each occurktimes in every row and column, so thatv=tk, is defined to be an equal frequency square. The properties of these squares are discussed and compared with the properties ofkLatin, Graeco-Latin or Hyper-Graeco-Latin squares of sidet.AvXvsquare for which thet<vletters occur in each row and column with frequencies proportional to the number of times they occur in the entire square is defined to be a proportional frequency square. The structure of the analysis of variance for several proportional frequency squares is developed and illustrated with an example of the analysis of data from three 5×5 proportional frequency squares with three treatments.