SYNOPSIS The first cladistic and Bayesian analyses of the trilobite families Lichidae Hawle & Corda, 1847 and Lichakepalidae Tripp, 1957 are presented. Thirty-one lichid genera and five lichakephalid outgroup taxa were coded for 48 characters using published descriptions. Two methods of phylogenetic inference were adopted: (1) a maximum-parsimony (MP) approach and, for the first time in a palaeontotogical context, (2) a Bayesian inference (BI) approach. The consensus trees from the MP and BI analyses were topologically similar, but differed principally in the deeper branches (i.e. the relationships between major clades). The Lichidae is monophyletic with respect to the Lichakephalidae in both analyses. The Trochurinae (Thomas & Holloway, 1988) is well supported by both analyses. Other groups are also supported (i.e. Tetralichinae, Echinolichinae and Platylichinae); two, however, are not (i.e. Homolichinae and Lichinae). A classification is proposed that represents the main branching pattern of the MP tree and also incorporates many elements of the BI tree, whilst applying least violence to the existing usage of the taxa. The Lichinae as defined here consists, therefore, of four main groups and these are given tribal status: Echinolichini, Tetralichini, Platylichini and Dicranopeltini. The last taxon is re-erected to contain those taxa formerly placed in the subfamily Lichinae. Lichas is assigned to a monogeneric tribe, the Lichini.