  The dynamical spin response of doped two-leg ladder antiferromagnets is
investigated based on the fermion-spin approach. Our calculations clearly
demonstrate a crossover from the incommensurate antiferromagnetism in the weak
interchain coupling regime to commensurate spin fluctuation in the strong
interchain coupling regime. In particular, the nuclear spin-lattice relaxation
rate extracted from the commensurate spin fluctuation decreases exponentially
with decreasing temperatures. The behaviors of the spin dynamics in the strong
coupling regime are quantitatively close to the experimental results of
Sr_{14-x}Ca_{x}Cu_{24}O_{41}.
