The New Institutional Sociology advocates that internal structures and procedures, including accounting, are influenced by external elements, thus organizations and accounting are led to incorporate socially institutionalized practices and procedures. In this sense, we can link the process of convergence to international accounting standards as the incorporation of socially institutionalized practices and procedures. Therefore, researching the challenges that countries have faced helps others to understand the obstacles that the convergence process imposes. Thus, the objective of this research is to verify which were the challenges that influenced the process of convergence to international accounting standards applied to the public sector in Brazil and Portugal. In Brazil, the challenges begin with encouraging greater participation of academia in the subject, from a critical point of view, accompanied by full disclosure, followed by greater adherence of Brazilian standards to international standards, aided by the disclosure of all assets and liabilities on an accrual basis, in addition to withstanding pressures in the political and cultural fields. In Portugal, the challenges begin with encouraging the training of Portuguese accountants who will have to deal with accounting based on principles, followed by the creation of institutional mechanisms that support pressures in the political and cultural fields, investing in the harmonization of local legislation so as to achieve greater comparability, accelerating the use of the SNC-AP in all Portuguese bodies and promoting the necessary accounting adjustments that inform the real value of the assets of the entities involved in the process.