Systematically different governments of different ideological matrices, make possible the development of affirmative actions in relation to the politics anti-racists in Brazil, favored for the spreading of the National Curricular Lines of direction for the Education of the Ethnic-Racial Relations and for Ensino de Histria and Cultura Afro-Brazilian and African, if anticipating in the search of forms that make possible one better agreement concerning positions aiming at to the convivncia in way to diversity. Thus being, this moment of our work makes a presentation of the content of these lines of direction and the related Law. Pertinent quarrel of questions racial in education Brazilian currently, although the universalizao of basic education, mainly for children of up to 14 years, when it is brought for Basic Ensino, obligatorily, children of six years of age, we still have many differences of accessibility and maintenance of black and white children in the public system of Brazilian education. According to Cavalleiro (2005), the black people in Brazil study 4,2 years on average, while for the whites this period if extends for 6,2 years. Already in the band of 14 and 15 years she has a 12% total more than the black illiterates in relation the whites of the same age, being that about 15% of the white children of 10 the 14 years of age are in the work market, against 40% of the black children.