We investigated charging effects in a small-area Josephson tunnel junction in a SQUID geometry, biased through high-resistance thin-film leads. The Josephson coupling energyE J was varied by an external magnetic flux inside the SQUID loop. At a certain value of the current the Zener tunneling rate exceeds that of dissipative relaxation and the system “jumps” from the lowest to higher Brillouin zones. The shape of I–V curve and crossover currentI cr are in good agreement with a theory of Zener tunneling with dissipation.