A new class of tests for fractional integration in the time domain based on M estimation is developed. This approach offers more robust properties against non-Gaussian errors than least squares or other estimation principles. The asymptotic properties of the tests are discussed under fairly general assumptions, and for different estimation approaches based on direct optimization of the M loss-function and on iterated k-step and reweighted LS numeric algorithms. Monte Carlo simulations illustrate the good finite sample performance of the new tests and an application to daily volatility of several stock market indices shows the empirical relevance of the new tests.