Conditions for exciting higher-harmonic electrostatic dust cyclotron waves in a collisional dusty plasma are investigated. Linear kinetic theory is used, and the effects of neutral–charged particle collisions are taken into account. In a plasma with negatively charged dust, electrostatic dust cyclotron waves can be driven unstable by ions drifting along the magnetic field. It is found that, under certain conditions, the critical ion drift for the excitation of higher-harmonic electrostatic dust cyclotron waves (i.e., ω ∼ mΩd, where m [ges ] 2 and Ωd is the dust cyclotron frequency) can be comparable to the critical drift for the excitation of the fundamental cyclotron harmonic (i.e., ω ∼ Ωd). Stability conditions are investigated for ranges of parameters that may be relevant to laboratory dusty plasmas.