Definition of a relevant market is the first and an essential step involved in determining whether or not there has been a contravention of certain of the substantive prohibitions under Part IV of the Trade Practices Act 1974 (Cth). The concept of a `market' for this purpose is based on settled, essentially economic, principles. However, proving the existence of a market, as a matter of evidence, in legal proceedings has been and remains a complex and uncertain exercise. The objectives of this thesis are to examine and critically evaluate the way in which the proof of markets under the Act has been handled in litigation before the Federal Court over the last 28 years. The primary sources for the research are the judgements that have been handed down by the Federal Court over this period in cases in which market definition has been a contested issue. While there is an abundance of literature on the relevant principles and their application in major cases, there has been no in-depth or systematic consideration of the issues of evidence and proof raised by this issue. For the purposes of examining the approach taken to the proof of a market, four principal categories of evidence are identified in the thesis - industry evidence, consumer evidence, quantitative evidence and expert opinion evidence. Issues of both form and substance that have arisen and the use that has been made of each category of evidence are explored in detail. For the purposes of evaluating the approach that has been taken to the proof of a market, a test of purposiveness is applied in the thesis. The question is posed, in other words, whether proof of the market has been approached with a view to identifying the existence (or otherwise) of close constraints on the commercial conduct of the firm(s) in question in the proceeding. It is concluded that, of the four categories of evidence examined, industry evidence has been the most effective in the sense that it has had the greatest impact on findings made concerning the relevant market. Consumer evidence has been bedevilled by concerns as to admissibility and weight and has been regarded as being of limited relevance in any event. Quantitative evidence has generally been unavailable and when available has proven unpersuasive. Overcoming initial reservations, there have been efforts to maximise the value derived from expert opinion evidence, particularly that of economists. Nevertheless, as some of these efforts themselves attest, such evidence has taken the form of submission more than it has of evidence and accordingly its role has been limited. The emphasis that has been placed on industry evidence is consistent with a purposive approach to market definition. It is this evidence that best enables a court to identify the sources and the extent of the constraints operating on the firm(s) in question. However, as is argued in this thesis, there are several important respects in which the analysis of industry evidence could and, indeed, should be more rigorously undertaken. Such rigour is required to ensure that markets are defined in a manner that reflects commercial realities and ultimately therefore to ensure that the substantive prohibitions under the Act are properly enforced.