The Korteweg-de Vries-Burgers (KdV-Burgers) equation and modified Korteweg-de Vries-Burgers equation are derived in strongly coupled dusty plasmas containing nonthermal ions and Boltzmann distributed electrons. It is found that solitary waves and shock waves can be produced in this medium. The effects of important parameters such as ion nonthermal parameter, temperature, density and velocity on the properties of shock waves and solitary waves are discussed.