We present a molecular dynamics study of the collective correlation functions of a hard-core system with an attractive Yukawa tail, for various thermodynamic states in the fluid and liquid regions of the phase diagram. The results are compared with available information for hard spheres. The small-q behavior of the intermediate scattering functions indicates the propagation of sound waves, i.e., phononlike collective excitations, in the hard-core Yukawa system. The upper limit of q for these collective modes is practically independent of the thermodynamic state. The computed transverse current correlation functions show that at liquid densities the hard-core Yukawa system is able to sustain shear wave propagation above a critical q; the upper limit of cl for sound waves and the lower limit for shear waves nearly coincide. All of these features are qualitatively similar to those found for hard spheres. However, there are significant quantitative differences, which reflect the influence of the attractive Yukawa tail on the dynamical behavior of the system.