How rich is the class of processes which are infinitely divisible with respect to time?

We give a link between stochastic processes which are infinitely divisible with respect to time (IDT) and Lévy processes. We investigate the connection between the selfsimilarity and the strict stability for IDT processes. We also consider a subordination of a Lévy process by an increasing IDT process. We introduce a notion of multiparameter IDT stochastic processes, extending the one studied by Mansuy [2005. On processes which are infinitely divisible with respect to time. arXiv:math/0504408.]. The main example of this kind of processes is the Lévy sheet.