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 trans- fers 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 dephosphory- lating the RR. The phosphatase activity may also be modulated by environmental signals. Using the EnvZ/ OmpR system as an example, we constructed math- ematical 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. Addi- tionally, for bistability to exist the major dephospho- rylation flux of the RR must not depend on the unphosphorylated SK. Structural modelling and pub- lished affinity studies suggest that the unphosphory- lated 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.