Advanced medical technology, though primarily a problem-solver, is also a problem-generator. Its progress confronts us with ever new problems of decision and with the problem of giving these decisions a sound ethical backing. The challenge for philosophy is, in this situation, to act as a kind of go-between: It should make a serious attempt to mediate between innovative medical technology and popular scepticism, and it should provide intellectual guidance for a structured and rational debate. Brain tissue transplantation is confronted mainly with two ethical problems: 1. Under which conditions are we justified to take transplantable brain tissue from aborted human embryos or fetuses? 2. Is it acceptable that the implantation of brain tissue taken from a human embryo or fetus might disturb, in one way or other, the identity of the recipient? To answer these questions, difficult anthropological issues must be discussed: 1. What are the criteria of death applying to embryos and fetuses? 2. What are the conditions for saying that the identity of a person is changed? The present contribution makes an effort to clarify the latter question. It examines the concept of identity in the context of brain tissue transplantation, makes a distinction between identity of personality and personal identity, and argues that even major changes of personality resulting from brain tissue transplantation would not by themselves amount to a change in personal identity. This result has to be reconsidered, however, in the light of the fact that brain tissue transplantation alters the make-up of the recipient's brain.(ABSTRACT TRUNCATED AT 250 WORDS)