During 1970-1971 the University of Lancaster Library Research Unit carred out a study of the extent to which leading British research libraries tend to duplicate rather than complement each others holdings. This investigation was commissioned in order to provide pertinent background information for the staff of the National Libraries ADP Study[1]. The investigation was in two parts, "National Catalogue Coverage Study" which estimated the overlap in holdings [2] and a "Foreign Books Acquisitions Study" which estimated the extent of duplication in the acquisition of non-British imprints [3]. The authors of this paper collaborated in the design and direction of the investigation. Several methodological problems were encountered. The purpose of this paper is to identify and discuss methodological difficulties in this specialist type of library survey. Examples of findings from the British study and from subsequent surveys in Indiana are given by way of illustration. The initial impetus was a major study of the overlap in holdings between 23 British libraries including the leading national and academic libraries. It became apparent that there were severe methodological problems involved. Since then it has seemed increasingly clear that: (i) When formulated in a general way. overlap is a widely occurring parameter in the bibliographical area whether in automated information processing or manual, (ii) The overlap parameter is likely to often be a critical one from the management point of view, especially in ascertaining the probable costs and benefits of automation, collaboration or, most of all, in collaboration in automation, (iii) Overlap studies are becoming more frequent on account of (i) and (ii). Therefore this paper has been prepared with the emphasis on the methodological aspects rather than the results of either of the actual surveys. © 1975.