A series of three lexical decision experiments showed that interlingual homographs may be recognized faster than, slower than, or as fast as monolingual control words depending on task requirements and language intermixing. In Experiment 1, Dutch bilingual participants performed an English lexical decision task including English/Dutch homographs, cognates, and purely English control words. Reaction times to interlingual homographs were unaffected by the frequency of the Dutch reading and did not differ from monolingual controls. In contrast, cognates were recognized faster than controls. In Experiment 2, Dutch participants again performed an English lexical decision task on homographs, but, apart from nonwords, Dutch words were included which required a “no” reaction. Strong inhibition effects were obtained which depended on the relative frequency difference of the two readings of the homograph. These turned into frequency-dependent facilitation effects in Experiment 3, where participants performed a general lexical decision task, responding “yes” if a word of either language was presented. It is argued that bilingual word recognition models can only account for the series of experiments if they explain how lexical processing is affected by task demands and stimulus list composition.