By middle childhood, the same genetic factors are largely responsible for individual differences in verbal and nonverbal abilities, suggesting a genetic basis for general cognitive ability (“g”). Our previous work on verbal and nonverbal abilities throughout the normal range of variation during infancy and early childhood suggests that genetic influences show domain-specific as well as domain-general effects, implying that the switch to nearly complete domain-general effects occurs later in development. Much less is known about the genetic structure of low cognitive performance, although our previous work has shown that a composite measure of low “g” is highly heritable at 2, 3 and 4 years of age. We report the first multivariate, longitudinal analyses of low verbal and nonverbal cognitive abilities (defined as the lowest 10% of the distribution) at 2, 3 and 4 years of age using data from 9026 pairs of UK twins assessed by their parents as part of the Twins Early Development Study (TEDS). Domain-general genetic influences increased significantly from 2 to 3 to 4 years. Although the phenotypic polychoric correlation between low verbal and low nonverbal ability was similar at 2, 3 and 4 years (.36, .43, .35), the genetic contribution to the phenotypic correlation increased dramatically (.37, .47, .76), with a corresponding decrease in the comorbid influence of shared environment (.61, .44, .35). We conclude that for low ability, as well as for normal variation in ability, genetic “g” emerges during early childhood but is not fully developed until middle childhood.