A nonlinear substructuring control (NLSC) method is developed as a more generalised form of linear substructuring control (LSC) by incorporating nonlinear signal-based control (NSBC) into a dynamical substructuring system (DSS). An advantage of NLSC is that it can be designed using the linearized models of the substructured systems without the need for accurate nonlinear dynamic models. In this study, the use of the NLSC method is demonstrated via substructured tests on nonlinear physical and numerical substructures. A series of substructuring tests were also conducted on a test rig, constructed within the ACTLab at the University of Bristol, which incorporated a pure time delay of 6.0 ms due to the presence of discrete-time elements. In the substructured tests, a trilinear hysteresis with piecewise linearity, commonly used in structural engineering, was embedded into the numerical substructure as the nonlinearity. The NLSC method was found to achieve stable and reliable substructured responses, even when the substructured systems had significant nonlinearity as well as the pure time delay term.