We have found that although the magnetic penetration depth lambda increases linearly in H in YNi2B2C, lambda in Y(Ni0.8Pt0.2)(2)B2C was found to be independent of H for Hless than or equal to0.4H(c2), suggesting that the superconducting gap is effectively isotropic. These results are consistent with the change in the structure of order parameter suggested by photoelectron spectroscopy. However, lambda in the Pt-doped sample is about 1.27 times larger than that estimated for an impurity effect, suggesting that the quasi-particles are not completely localized inside the vortex cores. Crown Copyright (C) 2002 Published by Elsevier Science B.V. All rights reserved.