Creativity involves generating novel and valuable ideas. While the importance of creative thinking is widely acknowledged, its cognitive basis is poorly understood, particularly in older adults. This study aimed to develop and test an explanatory model of creative thinking to elucidate its underlying cognitive functions in an elderly sample. The role of demographic variables, including age, multilingualism, socioeconomic status (SES), level of education, and gender in creative thinking was also investigated. One hundred and twenty‐five participants aged 65 years and above‐completed measures of divergent, convergent and associative thinking, as well as task‐switching, inhibition and fluid intelligence. Structural equation modeling (SEM) analyzed the relationships between these cognitive functions, and group differences assessed whether there were significant differences in the cognitive measures based on the demographic variables. Creative thinking appeared to entail the cooperation between divergent and convergent thinking, which both rely on associative thinking, suggesting an associative basis of creative thinking. Creative thinking involved fluid intelligence and task‐switching, but not inhibition, recasting it as a higher‐order function. This study supports the dual‐process account of creative thinking by demonstrating an associative basis and the role of executive functions. Differences among education and SES groups occurred for most cognitive functions analyzed. These findings inform prevailing theoretical frameworks of creative thinking.