Bacterial two-component systems (TCS) are key signal transduction networks regulating global responses to environmental change. Environmental signals may modulate the phosphorylation state of sensor kinases (SK). The phosphorylated SK transfers the phosphate to its cognate response regulator (RR), which causes physiological response to the signal. Frequently, the SK is bifunctional and, when unphosphorylated, it is also capable of dephosphorylating the RR. The phosphatase activity may also be modulated by environmental signals. Using the EnvZ/OmpR system as an example, we constructed mathematical models to examine the steady-state and kinetic properties of the network. Mathematical modelling reveals that the TCS can show bistable behaviour for a given range of parameter values if unphosphorylated SK and RR form a dead-end complex that prevents SK autophosphorylation. Additionally, for bistability to exist the major dephosphorylation flux of the RR must not depend on the unphosphorylated SK. Structural modelling and published affinity studies suggest that the unphosphorylated SK EnvZ and the RR OmpR form a dead-end complex. However, bistability is not possible because the dephosphorylation of OmpR∼P is mainly done by unphosphorylated EnvZ. The implications of this potential bistability in the design of the EnvZ/OmpR network and other TCS are discussed.