The reversible magnetization M(T,H) in high quality single crystals of Lu(N
i1-xCox)(2)B2C with x=0-0.09 is measured in a broad T,H domain and interpre
ted within London theory corrected for nonlocality of the current - vector-
potential relation. Profound deviations in the data from the standard Londo
n result, M proportional to ln(H-c2/H) in intermediate fields H(c1)much les
s than H much less than H-c2, are seen in clean samples at low T's. Unlike
strongly anisotropic high-T-c compounds, for nearly isotropic borocarbides
this behavior cannot be attributed to fluctuations of weakly interacting pa
ncake vortices. We show that the nonlocal London model describes qualitativ
ely and consistently the whole set of M(T,H) data and, in particular, its t
emperature and the mean-free path dependence. The scaling field H-0, which
arises in M=M(H/H-0) due to nonlocality, is found to be nearly proportional
to the the field H-2 at which the vortex lattice undergoes the symmetry ch
ange (the "square-tohex" transition).