Congruency sequence effects are observed when the congruency effects following incongruent trials are smaller than those following congruent trials. It is typically assumed that such flexible adjustments are evidence of cognitively controlled dynamic modulations. The present study investigated whether cognitive control acts locally or globally when implicit and explicit conflicts exist simultaneously within a system. The implicit SNARC task and explicit Simon task were combined in a single task. The results showed that congruency effects of one type (e.g., SNARC effect) were only smaller following an incongruent trial of the same type (e.g., SNARC effect), but not when following an incongruent trial of the other type (e.g., Simon effect). These results indicate the operation of local control mechanisms triggered by implicit and explicit conflicts.