The viscoelastic behavior of concentrated dispersions of adhesive hard spheres was investigated. By changing the temperature, the interaction potential of the particles was varied from a hard sphere repulsion to a strong attraction. Using torsion resonators and a nickel tube resonator the complex viscosity was measured in the frequency range 70-250 000 Hz. The results were described on the basis of a simple mechanical model in terms of a series of relaxation times and a single relaxation strength. The temperature dependence of the longest relaxation time and the relaxation strength indicated that the system undergoes a kinetic transition with decreasing temperature. The transition could be identified with the percolation threshold. Above the transition temperature where the dispersion is in a stable, fluid state, linear viscoelastic behavior is observed. Below the percolation threshold but still in the one-phase region, nonlinear viscoelasticity was measured, even at the smallest strains.