Most often bond orders have heuristically been defined. In this work we follow a rigorous theoretical procedure looking for an appropriate definition of this concept. The study points out the exchange part of the pair density as a suitable starting point to set up a bond order definition, while the definitions based on the fluctuation of electron populations should be restricted to noncorrelated state functions. Numerical calculations are reported to illustrate these conclusions. (C) 2003 Elsevier Science B.V. All rights reserved.