The well known fact that the product of two normal supersoluble subgroups is not in general supersoluble makes interesting the study of factorized groups whose subgroup factors are connected by certain permutability properties. In particular, \textit{M. Asaad} and \textit{A. Shaalan} [in Arch. Math. 53, No. 4, 318-326 (1989; Zbl 0685.20018)] introduced the notion of totally permutable product and obtained results in this direction. \textit{A. Ballester-Bolinches, M. C. Pedraza-Aguilera} and \textit{M. D. Pérez-Ramos} [Bull. Aust. Math. Soc. 53, No. 3, 441-445 (1996; Zbl 0886.20014)] and \textit{A. Ballester-Bolinches} and \textit{M. D. Pérez-Ramos} [J. Algebra 182, No. 3, 738-747 (1996; Zbl 0855.20018)] generalized these results in the finite universe through the theory of formations. In this paper, the authors analyze the behaviour of totally permutable products whose factors are torsion subgroups of the group. Some interesting facts about the structure of the group from that of the factors are proved. In fact it provides a valuable improvement in the knowledge of the structure of this kind of products by getting that in a totally permutable product of two torsion subgroups, the nilpotent residual of each factor centralizes the other factor. Other results are shown on the existence of normal subgroups, the embedding of the intersection, and the commutator subgroup of the two factors.