  Contact geometry allows to describe some thermodynamic and dissipative
systems. In this paper we introduce a new geometric structure in order to
describe time-dependent contact systems: cocontact manifolds. Within this
setting we develop the Hamiltonian and Lagrangian formalisms, both in the
regular and singular cases. In the singular case, we present a constraint
algorithm aiming to find a submanifold where solutions exist. As a particular
case we study contact systems with holonomic time-dependent constraints. Some
regular and singular examples are analyzed, along with numerical simulations.
