  Properties of the functional classes of star-product elements associated with
higher-spin gauge fields and gauge parameters are elaborated. Cohomological
interpretation of the nonlinear higher-spin equations is given. An algebra
${\mathcal H}$, where solutions of the nonlinear higher-spin equations are
valued, is found. A conjecture on the classes of star-product functions
underlying (non)local maps and gauge transformations in the nonlinear
higher-spin theory is proposed.
