SUMMARY The concept of orthogonality of experimental designs and the factors of a design has been discussed by numerous authors and defined in a variety of ways which in general are equivalent. The analysis of experimental designs is simplified by the property of orthogonality. Nonorthogonal designs are usually analyzed by the method of reduction or adjustment of factors. Eccleston & Russell (1975) introduced the concept of orthogonality of adjusted factors. This is defined more generally here and several theorems are presented. It is shown that these results can be used to simplify the analysis of nonorthogonal designs, many of which exhibit some degree of adjusted orthogonality.