Purpose – The present study discussed wave propagation in a nonlocal generalized thermoelastic half-space with moving an internal heat source under influence of rotation. Design/methodology/approach – Normal mode analysis is introduced to obtain the analytical expressions of the physical quantities. Findings – Numerical results are presented graphically to explore the effects of rotation, the nonlocal parameter, and the time-delay on the physical quantities. It is found that the physical quantities are affected by rotation, the nonlocal parameter, and the time-delay. Originality/value – The problem is solved based on the classical-coupled theory, the Lord–Shulman theory, and the Green–Lindsay theory with memory-dependent derivative (MDD).