Cognitive processes associated with frontal lobe functioning are often termed "executive functions." Two such processes are initiation and inhibition or the starting and stopping of responses. It has recently been claimed dysfunction of executive abilities can be explained by a single measure of fluid intelligence. Here, we test this claim, specifically for the executive abilities of response initiation and inhibition, across the healthy lifespan. In a cohort of 336 healthy adults (18-89 years), initiation and inhibition were assessed with the Hayling test, Stroop test, and phonemic and semantic verbal fluency. All participants also completed a measure of fluid intelligence. The relationship between fluid intelligence and executive measures was explored across the lifespan using a continuous approach. Mediation models were computed to assess whether age-related decline across the four initiation/inhibition tasks could be fully explained by a single measure of fluid intelligence. Age was negatively correlated with response initiation/inhibition and fluid intelligence. The mediation analyses identified only partial mediation of fluid intelligence for age and Hayling performance. By contrast, fluid intelligence did not mediate performance on the Stroop test or phonemic and semantic verbal fluency. Response initiation/inhibition are not able to be explained by fluid intelligence. The results support a multifactorial theory of executive functions and provide evidence for the inclusion of multiple specific executive measures in a thorough neuropsychological assessment of age-related cognitive decline.