The purpose of this paper is to present the properties of invariance for the interaction of fast electrons with a crystal and to deduce from them some symmetry rules for the interpretation of diffracting patterns or images. The small-angle approximation leads to a transformation of the propagation direction variable z into a time-like parameter. The symmetry operations which maintain z act as unitary operators and those which reverse z act as antiunitary operators. (C) 2002 Elsevier Science B.V All rights reserved.