  A simple formula for one-loop logarithmic divergences on the background of a
two-dimensional curved space-time is derived for theories for which the second
variation of the action is a nonminimal second order operator with small
nonminimal terms. In particular, this formula allows to calculate terms which
are integrals of total derivatives. As an application of the result, one-loop
divergences for the higher spin fields on the constant curvature background are
obtained in a nonminimal gauge, which depends on two parameters. By an explicit
calculation we demonstrate that with the considered accuracy the result is
gauge independent. Moreover, the result appeared to be independent of the spin
$s$ for $s\ge 3$.
