Occasionally, the expected effects of approach-avoidance motivation on anterior EEG alpha asymmetry fail to emerge, particularly in studies using affective picture stimuli. These null findings have been explained by insufficient motivational intensity of, and/or overshadowing interindividual variability within the responses to emotional pictures. These explanations were systematically tested using data from 70 students watching 5 types of affective pictures ranging from very pleasant to unpleasant. The stimulus categories reliably modulated self-reports as well as the amplitude of late positive potential, an ERP component reflecting orienting toward motivationally significant stimuli. The stimuli did not, however, induce expected asymmetry effects either for the sample or individual participants. Even while systematic stimulus-dependent individual differences emerged in self-reports as well as LPP amplitudes, the asymmetry variability was dominated by stimulus-independent interindividual variability. Taken together with previous findings, these results suggest that under some circumstances anterior asymmetry may not be an inevitable consequence of core affect. Instead, state asymmetry shifts may be overpowered by stable trait asymmetry differences and/or stimulus-independent yet situation-dependent interindividual variability, possibly caused by processes such as emotion regulation or anxious apprehension.