When humans perceive speech sounds, they categorize the sounds into one or another phoneme category. Perception of speech sound depends on context. Previous studies on categorical perception of lexical tones were mainly done in an absolute manner without context. In these experiments we explore the influence of context on the categorical perception of lexical tones. In particular, we ask whether the position of the context with respect to the target syllable influences the categoricalness of the perception. Two experiments on natural and synthesized speech both show that categorical boundaries of identification curves are sharper when the context is to the right of the target syllable than when the context is to the left of the target syllable. Moreover, steeper peaks are obtained in the discrimination curve from right context continuum. They agree with and enhance the identification results. Explanations of the phenomenon are suggested in the paper.