  The effect of a high--frequency microwave irradiation on the averaged
stationary charge in a single--electron tunneling box (SET--box) with
superconducting island is investigated. The resulting $\langle Q\rangle$--$Q_g$
characteristics are modified compared with those from the well--known constant
voltage--driven box. It can be shown that there is a cross--over from the
2e--periodic regime in $Q_g$ corresponding to the parity effect to 1e--periodic
behavior not only with increasing temperature but also with increasing
irradiation amplitude.
