SUMMARY A nested row-column design has v treatments arranged in b blocks each comprising pq units grouped into p rows and q columns. A class of designs based on a cyclical method of construction is defined. The canonical efficiency factors of such nested generalized cyclic row-column designs are examined. Efficient designs are tabulated for 5 < v < 15, p < 3, q < 7 and r < v, where r = bpq/v is the number of replications of each treatment. Row-column designs are used to eliminate heterogeneity in two directions. More generally, an experiment may have several blocks each containing pq plots arranged in p rows and q columns, where the blocks may represent a further blocking factor or provide replications of the basic row-column design. These designs are called nested row-column designs, since rows and columns are nested within blocks. The lattice square designs, introduced by Yates (1940), are examples of such designs. A general analysis and the concept of balance have been considered by Singh & Dey (1979). Several series of balanced nested row-column designs have been given by Singh & Dey (1979), Street (1981) and Agrawal & Prasad (1982a). Preece (1967) provides a table of nested balanced incomplete block designs and a number of these designs can also be used as balanced nested row-column designs. Other series based on partially balanced designs have been given by Street (1981) and Agrawal & Prasad (1982b). Jarrett & Hall (1982) gave some examples of small designs based on cyclic and generalized cyclic methods of con- struction, which they suggested could provide useful alternatives to nearest neighbour designs and methods. As an example of a balanced nested row-column design, consider the following design, given by Singh & Dey (1979), for five treatments 0, 1, 2, 3, 4 arranged in five blocks of two rows and two columns: