  Spectral boundary conditions for Laplace-type operators, of interest in
string and brane theory, are partly Dirichlet, partly Neumann-type conditions,
partitioned by a pseudodifferential projection. We give sufficient conditions
for existence of associated heat trace expansions with power and power-log
terms. The first log coefficient is a noncommutative residue, vanishing when
the smearing function is 1. For Dirac operators with general well-posed
spectral boundary conditions, it follows that the zeta function is regular at
0. In the selfadjoint case, the eta function has a simple pole at zero, and the
value of zeta as well as the residue of eta at zero are stable under
perturbations of the boundary projection of order at most minus the dimension.
