A statistical method for identification of nonlinearity in time series is discussed. The approach is based on Monte Carlo simulations and bootstrapping. Artificial surrogate series are generated, which are consistent with a range of null hypotheses that include linearity. In this way, the distribution of test statistics, that are computed for the original data, can be empirically estimated by an ensemble of surrogates. If a test statistic is out of range of its estimated distribution, then the corresponding null hypothesis is rejected, and nonlinearity can be assumed. However, other data characteristics, like nonstationarity, may bias the test result. Thus, surrogates should feature these characteristics as well. By means of surrogate data, nonlinear dependencies can be detected both within time series and between them. The surrogate algorithms are applied to different simultaneously measured time series taken from a diesel combustion engine. The complexity of choosing an appropriate surrogate method is demonstrated for different setups of the engine.