Ritter & Salamini (1996) presented a systematic account of two-point linkage analysis in allogamous diploid plant species. Vowden et al. (1995) described an alternative approach that is implemented in a computer program LINKEM. This paper describes how the latter approach has been extended to three-point linkage analysis, and implemented in a new program LINK3EM that is available from the authors. The essence of the approach is for the computer program to derive the appropriate form of analysis for a specific cross from its ‘knowledge’ of the most general type of cross that can arise. This avoids the need for programming specific codes for the many different types of cross that can arise. The program allows different locus orderings and parental phases to be compared. The Haldane or Kosambi map functions can be specified, although it is also possible to estimate all three pairwise recombination fractions without any assumed map function.