Imprecise multinomial processes: an overview of different approaches and how they are related to each other In this overview, we present and compare four different approaches to imprecise multinomial processes, which are generalizations of the classical multinomial process to the field of imprecise probability theory. Within this field, one can choose between a number of different mathematical frameworks. Amongst the most important ones, we have credal sets, coherent lower previsions and coherent sets of desirable gambles. We show how each of them can be used to model beliefs about the outcome of a single experiment. We give an overview of different ways of extending these local models to describe an infinite sequence of experiments, leading to four different types of imprecise multinomial processes. We investigate their properties, discuss the assumptions that underly them and show how they can be related to one another by imposing additional requirements. In particular, it turns out that by additionally imposing exchangeability, all four types of imprecise multinomial processes coincide, which ultimately provides us with a behavioural justification for applying sensitivity analysis to classical multinomial processes.