AbstractWe introduce Euler–Lagrange–Herglotz equations on Lie algebroids. The methodology is to extend the Jacobi structure from$$TQ\times \mathbb {R}$$TQ×Rand$$T^{*}Q \times \mathbb {R}$$T∗Q×Rto$$A\times \mathbb {R}$$A×Rand$$A^{*}\times \mathbb {R}$$A∗×R, respectively, whereAis a Lie algebroid and$$A^{*}$$A∗carries the associated Poisson structure. We see that$$A^*\times \mathbb {R}$$A∗×Rpossesses a natural Jacobi structure from where we are able to model dissipative mechanical systems on Lie algebroids, generalizing previous models on$$TQ\times \mathbb {R}$$TQ×Rand introducing new ones as for instance for reduced systems on Lie algebras, semidirect products (action Lie algebroids) and Atiyah bundles.