This paper is concerned with the classical Timoshenko system for vibrations of thin rods. It has been studied by many authors and most of known results are concerned with decay rates of the energy, controllability and numerical approximations. There are just a few references on the long-time dynamics of such systems. Motivated by this scenario we establish the existence of global and exponential attractors for a class of semilinear Timoshenko systems with linear frictional damping acting on the whole system and without assuming the well-known equal wave speeds condition.