  We present theoretical and experimental studies of resonant localized
resistive states in a Josephson junction ladder. These complex breather states
are obtained by tuning the breather frequency into the upper band of linear
electromagnetic oscillations of the ladder. Their prominent feature is the
appearance of resonant steps in the current-voltage (I-V) characteristics. We
have found the resonant breather-like states displaying incommensurate
dynamics. Numerical simulations show that these incommensurate resonant
breathers persist for very low values of damping. Qualitatively similar
incommensurate breather states are observed in experiments performed with
Nb-based Josephson ladders. We explain the appearance of these states with the
help of resonance-induced hysteresis features in the I-V dependence.
