Williams Syndrome is a rare genetic syndrome, which exhibits an uneven cognitive profile. In adults with Williams Syndrome, the profile is of impaired visuo-spatial skills, number concepts, and problem solving, with good language and face processing skills. Recent research has shown that language and face processing are not 'preserved' abilities, in that the processes involved differ from those used by normal controls. Down's syndrome is a more common genetic syndrome, with a relatively level cognitive profile. The purpose of this thesis was to examine aspects of visual cognition in infants and young children with Williams and Down's syndromes, to determine whether the cognitive profile found in adults is present from infancy, or whether the end state is a product of the relationship between impaired systems interacting in an aberrant way with environmental factors. Four groups of infants and young children were recruited and tested on a range of measures of visual cognition: children with Williams syndrome, children with Down's syndrome, chronological age matched controls, and mental age matched controls. All children were tested with the Bayley Scales of Infant Development II, in order to obtain a general measure of development for matching purposes. The experimental tasks given to all four groups examined face processing, saccade planning, sustained attention, and temperament. Relationships between measures were also examined. The results indicate that the pattern of impairments found in adults with Williams syndrome are not wholly reflected in infancy. Although precursors of impairment were found for some domains, other areas of difficulty experienced in adulthood were not found in infancy. Findings are discussed in terms of the impact of impairments on the development of other cognitive abilities, and methodological problems in testing atypically developing infants are considered.