The health-related quality of life (HRQoL) literature presents a confused picture of what 'equivalence' in the cross-cultural use of HRQoL questionnaires means and how it can be assessed. Much of this confusion can be attributed to the 'absolutist' approach to the cross-cultural adaptation of HRQoL questionnaires. The purpose of this paper is to provide a model of equivalence from a universalist perspective and to link this to the translation and adaptation of HRQoL questionnaires. The model evolved from reviews of the HRQoL and other literatures, interviews and discussions with researchers working in HRQoL and related areas and practical experience in the adaptation and development of HRQoL instruments. The model incorporates six key types of equivalence. For each type of equivalence the paper provides a definition, proposes various strategies for examining whether and how types of equivalence can be achieved, illustrates the relationships between them and suggests the order in which they should be tested. The principal conclusions are: (1) that a universalist approach to the cross-cultural adaptation of HRQoL instruments requires that six types of equivalence be taken into account; (2) that these are sufficient to describe and explain the nature of the cross-cultural adaptation process; (3) that this approach requires careful qualitative research in target cultures, particularly in the assessment of conceptual equivalence; and (4) that this qualitative work will provide information which will be fundamental in deciding whether to adapt an existing instrument and which instrument to adapt. It should also result in a more sensitive adaptation of existing instruments and provide valuable information for interpreting the results obtained using HRQoL instruments in the target culture.