This is a report of monoamniotic-monochorionic (ie, probably MZ) twins, one of which had anencephaly, whereas the co-twin died of complications of prematurity. Autopsy in this seemingly nonmalformed twin showed a small encephalocele. The literature on MZ twins with discordant anencephaly is often contradictory. It is suggested that this might be due to the difficulty of determining zygosity on the one hand and identifying discordance or concordance on the other. This case is presented as an example of this difficulty; it is discordant with respect to anencephaly, but concordant in the sense of "dysraphic" disturbances.