It is a central assumption that larger bodies require larger brains, across species but also possibly within species with continuous growth throughout the lifetime, such as the crocodile. The current study investigates the relationships between body growth (length and mass) and the rates of growth of various subdivisions of the central nervous system (CNS) (brain, spinal cord, eyes) in Nile crocodiles weighing between 90 g and 90 kg. Although the brain appears to grow in two phases in relation to body mass, initially very rapidly then very slowly, it turns out that brain mass increases continuously as a power function of body mass with a small exponent of 0.256, such that a 10-fold increase in body mass is accompanied by a 1.8-fold in brain mass. Eye volume increases slowly with increasing body mass, as a power function of the latter with an exponent of 0.37. The spinal cord, however, grows more rapidly in mass, accompanying body mass raised to an exponent of 0.54, and increasing in length as predicted, with body mass raised to an exponent of 0.32 (close to the predicted 1/3). While supporting the expectation formulated by Jerison that larger bodies require larger brains to operate them, our findings show that: (1) the rate of increase in brain size is very small compared to body growth; and (2) different parts of the CNS grow at different rates accompanying continuous body growth, with a faster increase in spinal cord mass and eye volume, than in brain mass. © 2013 Wiley Periodicals, Inc.