"Executive functions" (EF) is a multidimensional construct which encompasses many higher-order cognitive control operations, and is considered a potential mediator of age-associated changes in other cognitive domains. Here we examine the heritability of four measures of EF, and the genetic influences on their covariation with general cognitive abilities (GCA) from the Older Australian Twins Study. Participants included 117 pairs of monozygotic twins, 98 pairs of dizygotic twins, and 42 single twins, with a mean age of 71. Genetic modeling showed that additive genetic factors contributed to 59, 63,29, and 31% of the variance in the four measures: working memory, verbal fluency, response inhibition and cognitive flexibility, respectively. The phenotypic associations among the four EF measures were modest, which is in line with other evidence that EF is a multi-dimensional construct.All of the covariation between the EF measures was attributable to a common genetic factor. Similarly, all of the covariation between EF and General Cognitive Ability was explained by a common genetic factor, with no significant covariance due to environmental (E) factors. The genetic correlations between the measures were moderately high, suggesting that they may have common biological underpinnings. The genetic influence in the covariation of the EF measures and GCA also suggests that some aspects of EF and GCA share the same genes or same set of genes.