In this paper, we establish that any interval graph (resp. circular-arc graph) with n vertices admits a partition into at most ⌈log3n⌉ (resp. ⌈log3n⌉ + 1) proper interval subgraphs, for n>1. The proof is constructive and provides an efficient algorithm to compute such a partition. On the other hand, this bound is shown to be asymptotically sharp for an infinite family of interval graphs. In addition, some results are derived for related problems. © 2010 Wiley Periodicals, Inc. J Graph Theory 68:38-54, 2011 © 2011 Wiley Periodicals, Inc.