We consider two types of resonance phenomena in Josephson junctions, both r
elated to the existence of highly resolved levels of a quantum "particle" i
n a potential well. The existence of the levels is manifested in the most s
triking way in a resonance decrease of the lifetime of the metastable state
under the action of an alternating external current. A strong resonance sh
ould take place at the frequency equal to the level spacing. The second typ
e of resonance phenomena takes place;It such values of the bias current I,
for which two levels in adjacent wells happen to cross. The shape and size
of peaks depend strongly on the parameters of the junctions, as well as on
the temperature and number of resonance levels.