  The classical value of the Hamiltonian for a system with timelike boundary
has been interpreted as a quasilocal energy. This quasilocal energy is not
positive definite. However, we derive a `quasilocal dominant energy condition'
which is the natural consequence of the local dominant energy condition. We
discuss some implications of this quasilocal energy condition. In particular,
we find that it implies a `quasilocal weak energy condition'.
