The echo state network (ESN) is presented as the building block for the behavioural modelling of integrated circuits. The ESN is able to model the nonlinear relationships of time-domain signals observed in integrated circuit simulations. An adaptive algorithm for sampling the nonlinear behaviour of integrated circuits in the time-domain is proposed, that enables building ESN models that cover a wide range of operation of the modelled circuit. A nonlinear impedance model based on the echo state network is proposed. The model enables building interchangeable behavioural models of integrated circuits in the conducted immunity simulation environment according to the IEC-62132-4 Direct RF Power Injection (DPI) standard, and it is applied to a buffered voltage reference integrated circuit that consists of three subcircuits. An overview of nonlinear effects observed in the conducted immunity simulations of the modelled circuit is presented, and the methodology for evaluating the accuracy of the modelled time-domain waveforms is introduced. The stability of the presented behavioural models is analysed, including the DC operating point stability, the small-signal stability, and the initial transient stability. The behavioural modelling principles are also applied to modelling applications in ESD and EMC area. A lumped-distributed model of a transmission line pulsing setup is presented, including a behavioural model of an ESD protection device that exhibits snapback. The behavioural model of an I2C pad of an industrial integrated circuit is presented that enables simulating the RF re-radiation due to RF harmonic distortion in a magnetically coupled wireless system.