This paper aims to think about the possible points of contact between neoconcretism and minimal art, analyzed from two fundamental theoretical formulations on these movements: the notions of non-object and specific objects, elaborated by Ferreira Gullar and Donald Judd, respectively. These notions sought to conceptualize the new type of three-dimensional art object, and in both cases considered an overcoming of the traditional artistic media of painting and sculpture. In spite of the similarities between these notions, the validation of this new artistic production was made, for each group, in moments in which its relation with the heritage of European art history and the presence of modernism occurred in different ways. The analysis of these movements from their relations with modernism, therefore, reveals a series of textual layers linked to the construction of these groups of artists as movements, as well as to the criticism and history built on them - from its inception to the current days.