  In this document, we develop a new model for the category of dg-categories.
Following Rezk's example in the case of classic Segal spaces, we define
dg-Segal spaces: functors between free dg-categories of finite type and
simplicial spaces to which we add certain properties. We define also complete
dg-Segal spaces, and make their relationship to classic Segal spaces explicit.
With the help of two new hypercover constructions, and up to a certain
hypothesis, we prove that there exists an equivalence between the homotopy
category of dg-categories and the homotopy category of functors defined above
with a model structure making the complete dg-Segal spaces into its fibrant
objects.
