This paper provides a characterization of fibrant objects in the model category structures $\mathcal{ScCat}_c$ and $\mathcal{ScCat}_f$ for Segal categories. The main results show that Reedy fibrant Segal categories are precisely the fibrant objects in $\mathcal{ScCat}_c$, and Segal categories that are fibrant in the projective model structure on simplicial spaces are precisely the fibrant objects in $\mathcal{ScCat}_f$. The paper also discusses the definitions and properties of Segal categories, simplicial sets, and model category structures, including the Reedy and projective models. Key proofs involve demonstrating that fibrant objects in restricted model categories (with a fixed set in degree zero) are indeed fibrant in the more general models, using techniques such as pushouts and localization. The results are significant for understanding the homotopy theory of Segal categories and their applications in algebraic topology.This paper provides a characterization of fibrant objects in the model category structures $\mathcal{ScCat}_c$ and $\mathcal{ScCat}_f$ for Segal categories. The main results show that Reedy fibrant Segal categories are precisely the fibrant objects in $\mathcal{ScCat}_c$, and Segal categories that are fibrant in the projective model structure on simplicial spaces are precisely the fibrant objects in $\mathcal{ScCat}_f$. The paper also discusses the definitions and properties of Segal categories, simplicial sets, and model category structures, including the Reedy and projective models. Key proofs involve demonstrating that fibrant objects in restricted model categories (with a fixed set in degree zero) are indeed fibrant in the more general models, using techniques such as pushouts and localization. The results are significant for understanding the homotopy theory of Segal categories and their applications in algebraic topology.