A machine is described consisting of a universal non-linear filter, which is a highly adaptable analogue computer, together with a training device. The analogue machine has 18 input quantities from which it can compute in about 2 millisec 94 terms of a polynomial, each term containing products and powers of the input quantities, with adjustable coefficients, and can form their sum. The input quantities may be, for instance, 18 past samples of the values of a stochastic variable which is fed into the machine, and the result of the computation is an output function which contains 94 free variables. The training device optimizes the output by successive adjustment of the variable coefficients, until it has approached a target function as closely as can be achieved with a polynomial of 94 terms, by the criterion of the least mean-square error. This is done by repeatedly feeding into the machine a record of the stochastic process, long enough to be representative, and adjusting the variable coefficients, one at a time after each run, by a strategy which ensures that the error will monotonically decrease from run to run.In order to make the machine an optimum filter it is trained on a record of a noisy process, together with a target record which contains the signal only. It is taught as a predictor by taking as the target function a value of the stochastic process advanced by a certain time interval beyond the last value which goes into the input. It is trained as a simulator, for instance of an unknown mechanism, by feeding it with the input of the mechanism to be simulated at one end and presenting it at the other with its output as target function. The machine will then make itself into a model of the device to be simulated and the non-linear transfer function of the device can be read off from the final setting of the coefficients, as nearly as it can be represented by a 94-term polynomial. The machine is not confined to single-input systems.The machine incorporates 80 analogue multipliers of a novel ‘piezomagnetic’ type which, in its present form, can perform over 1000 multiplications per second with an error of 0.5% or less.A few examples of the first test applications of the machine are described.