The first of three documents on Project SEARCH (Search for Exceptional Abilities Reachable among Children with Handicaps) considers methods of detecting cognitive giftedness in exceptional children. It is explained that Catell's cognitive model of fluid intelligence is the basic premise used. Individual sections are presented on hearing impaired, physically handicapped, mentally retarded, learning disabled, mild behavioral problem, and severe behavioral problem children. Considered in these sections are the following aspects: the influence of the handicap on cognitive development, the influence of the handicap on the validity of the assessment, interpretation of formal test scores and responses, and interpretations of naturalistic observations. Among tests described are measures of verbal language skills (including the Detroit Test of Learning Aptitude and the Peabody Picture Vocabulary Test); nonverbal performance (such as the Leiter International Scale and the Columbia Mental Maturity Scale); visual spatial relations; sequencing and memory; and social perceptiveness and comprehension (such as the Thematic Apperception Test.) (CL)