  We present an analytic theory for the energy spectrum of a two-leg spin
ladder doped with two holes. Starting from a pseudo-fermion-bond-boson
representation of the corresponding $t_{1,2}-J_{1,2}$ Hamiltonian we apply a
diagrammatic approach adapted to the limit of strong rung coupling, which
includes both, the coupling of holes to the spin background as well as the
two-hole interactions. The two-hole spectrum is calculated and the formation of
bound states is discussed. Additionally the evolution of the spin gap of the
ladder upon doping is analyzed. A comparison with existing exact
diagonalization data is presented and good agreement is found.
