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In this study we apply modern methods for the search of strange attractor structures with low dimension to space plasmas. Together with an estima-tion of the correlation dimension, we include in our methods an estimation of the largest Lyapunov exponent and the development of reliable criteria for the exclusion of pseudochaotic dynamics caused by colored noises. The use of these methods in the analysis of magnetospheric and solar wind data gives strong evidence for low-dimensional chaotic dynamics. In par-ticular, our findings indicate a magnetospheric strange attractor with a fractal dimension df about 3.5 and a solar wind strange attrac ith a fractal dimension of about 4.5.