A study was conducted to clarify a number of issues related to Piaget's theory of invariant sequantiality in child cognitive development. Ss were 143 middle-class white children of bright, average and retarded psychometric abilities (measured by performance on the Stanford-Binet Intelligence Test). Bright and average Ss were chronologically aged 5-7 years; retarded Ss were mentally aged 5-7 years and chronologically aged 6-12 years. Tests were individually administered in four sessions totalling about three hours as follows: guessing game, conservation of mass, family egocentrism, egocentrism in left-right perspective, constancy of generic identity, class inclusion, conservation of number, constancy of sex role, conservation of substance in the ring segment illusion, realism and internal-external differentiation in development of the dream concepts, conservation of length, transitivity of length, conservation of liquid continuous quantity, magic interview, object sorting, and the Holtzman Inkblot Test. Procedures, scoring, and results are given for each test. (KM)