Abstract. On donne une caractrisation topologique des surfaces relles totalement algbriques parmi les surfaces bielliptiques. Ceci achve la dtermination des surfaces relles totalement algbriques parmi les surfaces de dimension de Kodaira nulle. On dcrit de plus un exemple de surface algbrique complexe qui n'est dformation quivalente aucune surface possdant une structure relle totalement algbrique non vide. Using topological data, we give a classification of totally algebraic real surfaces among all the bi-elliptic surfaces. Thus this work comletes the determination of totally algebraic real surfaces among all zero-Kodaira dimensional surfaces. Furthermore we give an example of a complex algebraic surface which is not deformation equivalent to any surface with nonempty totally algebraic structure.