In [26] I studied the problem of constructing the theory of
massless higher spin (
) fields on arbitrary curved background
spacetime. It is found that a consistent formulation of the theory of
higher spin fields on arbitrary curved background requires to give up the
locality of the theory. A gauge-invariant action functional for a quantum
massless gauge field in arbitrary background is constructed. This
functional is nonlocal but turns into the free local action when
the background fields vanish. As an application the gauge-invariant
covariant nonlocal actions for the spin-vector s=3/2 fields and for the
rank 2 tensor s=2 fields in arbitrary curved spacetime are explicitly
constructed, which turn into the standard local Rarita-Schwinger and
Pauli-Fierz ones in flat spacetime.