In Brazil, as in other parts of the world, one of the main forms used for the practice of fraud and corruption in the Public Administration is the contracting of works, the supply of goods and the provision of services. The amount of money involved in public contracting and spent on fraud and corruption are very high and could be well used to improve the quality of life of the population. This study aims to contribute to the problem as the main hypotheses of fraud and corruption in Brazilian public contracting are exposed and the risk indicators that public agents responsible for the control of the Public Administration, civil society organizations and citizens are exposed to. They must be attentive to identify situations of preparation or of present or past occurrence of these illicits.