In this paper, we investigate the Hyers–Ulam stability of nth order linear homogeneous and non-homogeneous dynamic equations with nonconstant coefficients on time scales by using open mapping theorem. Also we study the generalized Hyers–Ulam stability for nth order linear dynamic equations on time scales. Initially, we recall some basic results for the solutions of nth order dynamic equations with the help of Wronskians of n − 1 times differentiable functions on time scales. Secondly we make some assumptions for the generalized Hyers–Ulam stability of nth order linear dynamic equations on time scales. At the end, we give an example to illustrate our results.