Conflict-monitoring theory argues for a general cognitive mechanism that monitors for conflicts in information-processing. If that mechanism detects conflict, it engages cognitive control to resolve it. A slow-down in response to incongruent trials (conflict effect), and a modulation of the conflict effect by the congruence of the preceding trial (Gratton or context effect) have been taken as indicators of such a monitoring system. The present study (N = 157) investigated individual differences in the conflict and the context effect in a horizontal and a vertical Simon task, and their correlation with working memory capacity (WMC). Strength of conflict was varied by proportion of congruent trials. Coherent factors could be formed representing individual differences in speeded performance, conflict adaptation, and context adaptation. Conflict and context factors were not associated with each other. Contrary to theories assuming a close relation between working memory and cognitive control, WMC showed no relation with any factors representing adaptation to conflict.