The article studies the predictors of speech development at 3-4-year old children with autism. The study included 50 children at the age of 3-4 years (10 girls and 40 boys) diagnosed “autism spectrum disorder”, including 9 non-speaking children and 12 weak-speaking children who could use several-word phrases. The study used the CARS method to determine autism and A.R. Luria’s neuropsychological method to determine the children’s psychophysical development. The average psychological age for non-speaking children was determined with the LEITER-3 method and with the A. Binet-T.Simon method. A good convergence of the examination results received by both methods was obtained for the children with autism (the validity criterion - Cronbach's alpha was 0.75), which indicated the possibility to use the LEITER-3 method for the determination of autistic children’s psychological age. We found that the average mental development of children with autism was below their biological age, ranging from 4 months to 3 years and 5 months. On the basis of neuropsychological study of children with autism by A.R. Luria’s method and the CARS method, the development of verbal and non-verbal communication of the studied children was identified. The development of verbal and non-verbal communications depended on an autism degree: the worse autism is, the less developed are children’s speech abilities. The performed correlation and factor analyses allowed us to determine the predictors of communicative competence development for early-age children with autism. In particular, we has determined that neuropsychological indicators such as body possession, movements and actions, orientation, dynamic praxis, activity level, imitation, acoustic gnosis, and intellectual development are the predictors of further non-verbal communication development. The predictors of verbal communication are the following indicators: acoustic gnosis, visual reaction, sensory, object use, and a child’s intellectual development. Taking into account the specifics of the sensory perception and the information processing characteristic for the examined disorder, the sequence of speech therapists’ actions aimed at speech correction of children with autism is proposed.