Systematic methods for synthesising nonlinear networks having a prescribed scalar or multidimensional piecewise-linear function are described. In the scalar case, precision active-circuit building blocks using operational amplifiers, transistors, diodes, and resistors are given for realising piecewise-linear drivingpoint and transfer characteristic plots. In the multidimensional case, methods are given for realising a multiterminal nonlinear network having a multidimensional piecewise-linear transfer function. Finally, these methods are generalised for synthesising nonlinear n-ports having a prescribed multidimensional piecewiselinear driving-point function. Although most of the basic building blocks are grounded active networks, convertor networks are developed for transforming such grounded networks into floating networks having the same properties. By slight modifications of these convertor networks, other useful conversion properties are also presented