  The evolution of the spin gap of a 2-leg ladder upon doping depends upon the
nature of the lowest triplet excitations in a ladder with two holes. Here we
study this evolution using various numerical techniques for a t-t'-J ladder as
the next-near-neighbor hopping t' is varied. We find that depending on the
value of t', the spin gap can evolve continuously or discontinuously and the
lowest triplet state can correspond to a magnon, a bound magnon-hole-pair, or
two separate quasi-particles. Previous experimental results on the
superconducting two-leg ladder Sr12Ca2Cu24O41 are discussed.
