During mammalian development, one of the two X chromosomes in female embryos is randomly inactivated in the somatic cell in order to achieve gene dosage compensation. But is X inactivation established simultaneously or is it accomplished over time in a lineage-dependent fashion? We have examined this question in mouse embryos carrying an X-linked lacZ transgene. This transgene is subject to inactivation and the loss of beta-galactosidase activity provides a direct indication of X inactivation in individual cells. We find that X inactivation proceeds with different schedules in different somatic tissues, and the notochord, the heart, cranial mesoderm and the hindgut are among the last tissues to undergo X inactivation.