Backward crosstalk effects (BCE) are observed in dual-task studies when the characteristics of Task 2 (T2) influence Task 1 (T1) performance. One type of BCE, the no-go BCE, is reported when T2 is a go/no-go task. The usual observation is that when T2 is a no-go, T1 processing takes longer than when T2 is a go. No-go BCE is due to the response inhibition needed to inhibit an already prepared T2 response spilling over to T1 motor execution. Growing evidence shows that response inhibition causes affective devaluation of the associated stimuli due to the negative affect elicited by inhibition. It is unclear how no-go BCE based on response inhibition would interact with affective processing in T1. To test this, we recruited a dual-task paradigm, where T1 is a valence categorization task, and T2 is a go/no-go task. In Experiments 1 and 3, we presented positive and negative words as S1 and color (Experiment 1) and numbers (Experiment 3) as S2. In Experiment 2, we created an affective (mis)match between S1 (positive, negative, neutral) and S2 (high, low tone) through counterbalancing. Overall, we observed a large no-go BCE exclusively when Task 1 was positive but an absent or reversed no-go BCE when Task 1 was negative. Results are discussed in the context of an affective mismatch between S1 valence and T2 response type.