We present a study of the static polarizability for the tubular fullerenes C-60 + (i x 10), where i= 0-5, and the closely related [5,5] carbon nanotube, using time-dependent (current)-density-functional theory. Comparing the results obtained within the conventional adiabatic local-density approximation with those obtained using the Vignale-Kohn current-dependent exchange-correlation functional it is found that the extra long-range exchange-correlation effects described by the current-density functional are important to consider, especially for the longest fullerenes. For all systems studied the current-density functional results are in good agreement with experiment, and the agreement with available ab initio self-consistent-field results and results from a point-dipole interaction model is much better than when using the adiabatic local-density functional. (C) 2004 Elsevier B.V. All rights reserved.