Massive and massless behavior in dimerized spin ladders

We investigate the conditions under which a gap vanishes in the spectrum of dimerized coupled spin-1/2 chains by means of Abelian bosonization and Lan czos diagonalization techniques. Although both interchain (J') and dimeriza tion (delta) couplings favor a gapful phase, it is shown that a suitable ch oice of these interactions yields massless spin excitations. We also discus s the influence of different arrays of relative dimerization on the appeara nce of nontrivial magnetization plateaus.