Dear Georgios,
The general linear model used in SPM makes no assumptions about the distribution of the regressors (the X's in Y=X beta + epsilon). They are assumed to be fixed and known, measured without error. The distributional assumption concerns the errors (epsilon) which are assumed to be Gaussian.
What I can say is that the structure of the X's will affect how sensitive you are to *lack* of Gaussianity of the errors. For example, a balanced two-sample t-test has the greatest robustness to non-Gaussianity, while a highly unbalanced two-sample t-test (i.e., the worst case, singleton subject vs. a group) is highly sensitive to failures of the Gaussian assumption.
On the "measured without error" assumption: If there are errors in the X's, e.g. they are an noisy measure of behaviour or clinical state, then it's not so bad. The model will underestimate the magnitude of the true association (i.e. the estimated beta's will be smaller in absolute value than if you could use a noise-free version of the X's), but under the null hypothesis the inferences remain valid.
-Tom
