This work considers the existence of the global smooth solutions of several generalized BBM-Burgers equations. First, for n ≥1, the convergence results are discussed by employing a compact imbedding theorem. Following this, when n = 1, by exploiting the modified compact framework of Yunguang Lu, a convergence result is also obtained. Finally, it is pointed out that to get the strong convergence results, the second results do not ask f to be convex. This is due to the ...