  This paper is concerned with solution in H\"{o}lder spaces of the Cauchy
problem for linear and semi-linear backward stochastic partial differential
equations (BSPDEs) of super-parabolic type. The pair of unknown variables are
viewed as deterministic spatial functionals which take values in Banach spaces
of random (vector) processes. We define suitable functional H\"{o}lder spaces
for them and give some inequalities among these H\"{o}lder norms. The
existence, uniqueness as well as the regularity of solutions are proved for
BSPDEs, which contain new assertions even on deterministic PDEs.
