The robustness against strongly non-linear forms for the conditional variance of tests for detecting conditional heteroskedasticity using both artificial neural network techniques and bootstrap methods combined, is analysed in the context of ARCH-M models. The size and the power properties in small samples of these tests are examined by using out Monte-Carlo experiments with various standard and non-standard models of conditional heteroskedasticity. The P value functions are explored in order to select particularly problematic cases. Graphical presentations, based on the principle of size correction, are used for presenting the true power of the tests, rather than a spurious nominal power as it is usually made in the literature. In addition, graphics linking the process dynamics with the heteroskedasticity forms are shown for analysing in which circumstances the neural networks are effective.