Open p-branes

It is shown that many of the p-branes of type II string theory and d = 11 supergravity can have boundaries on other p-branes. The rules for when this can and cannot occur are derived from charge conservation. For example it is found that membranes in d = 11 supergravity and IIA string theory can have boundaries on fivebranes. The boundary dynamics are governed by the self-dual d = 6 string. A collection of N parallel fivebranes contains 1/2N(N - 1) self-dual strings which become tensionless as the fivebranes approach one another.