Nuclear magnetic resonance (NMR) on copper nuclei has been performed in the ladder system Sr(ZnxCu1-x)(2)O-3. The NMR lines for the Zn-doped samples (0.25%) show drastic broadening at low temperatures below 100 K. while not for the pure samples, The broadening is not explained by the free spins with short correlation length (xi/alpha similar to 3-4) which is expected in a spin-gap system, and suggests that the staggered moments are induced even on the sites far away from the impurities. (C) 1998 Elsevier Science B.V. All rights reserved.