A higher-order process calculus is a calculus for communicating systems which contains higher-order constructs like communication of terms. We analyse the notion of bisimulation in these calculi. We argue that both the standard de nition of bisimulation (i.e., the one for CCS and related calculi), as well as higher-order bisimulation AGR88, Bou89, Tho90] are in general unsatisfactory, because of their overdiscrimination. We propose and study a new form of bisimulation for such calculi, called context bisimulation, which yields a more satisfactory discriminanting power. A drawback of context bisimulation is the heavy use of universal quanti cation in its de nition, which is hard to handle in practice. To resolve this di culty we introduce triggered bisimulation and normal bisimulation, and we prove that they both coincide with context bisimulation. In the proof, we exploit the factorisation theorem: When comparing the behaviour of two processes, it allows us to \isolate" subcomponents which might give di erences, so that the analysis can be concentrated on them.