Electronic trading systems provide the computational support for stock exchanges. Liquid markets use order-driven systems, i.e., where client requests, for trading financial instruments, are served through individual orders. This paper presents Petri net models assembling some crucial processes executed within order-driven systems such as orders submission, application of precedence rules, and the order matching mechanism. Such processes were modelled as types of agents running in a multi-agent system (MAS) using nested Petri nets (NP-nets) - a convenient formalism for modelling MAS. With NP-nets, we focus on the control-flow perspective (causal dependence between activities executed by agents) and in the synchronization between agents. Conversely, we have used coloured Petri nets to extend the model including orders as objects with attributes. Thus, this work with Petri nets represents an experimental & initial research phase to validate trading systems using related methods such as process mining, simulations and model checking.