  The effect of a ring exchange on doped two-leg ladders is investigated
combining exact diagonalization (ED) and density matrix renormalization group
(DMRG) computations. We focus on the nature and weights of the low energy
magnetic excitations and on superconducting pairing. The stability with respect
to this cyclic term of a remarkable resonant mode originating from a hole
pair-magnon bound state is examined. We also find that, near the zero-doping
critical point separating rung-singlet and dimerized phases, doping reopens a
spin gap.
