This must be a naive question, but I'm wondering about the definition of the quasi-unipotent monodromy for general (not only 1-parameter families). The problem is that usually in the books of algebraic geometry quasi-unipotent monodromy is only discussed over a disc $\Delta ^{*}$ i.e. for a 1-parameter family. In this case we know that for a fibration $f: X \rightarrow \Delta$, with monodromy representation $\rho : \pi_{1}(\Delta^{*}) \rightarrow Aut(H^{i}(X_{0}))$, the image $\rho (T)$ of a generator $T$ of $\pi_{1}(\Delta^{*})$ is a quasi-unipotent matrix. What is the correct generalization of this to arbitrary families? For example, in multi-parameter case, it could happen that there are several generators $T_{i}$ such that each $\rho(T_{i})$ is a quasi-unipotent matrix but for example $\rho(T_{1})\rho(T_{2})$ is not quasi-unipotent . So is the possible generalization is that all of the matrices in the monodromy group (image of the monodromy representation) should be quasi-unipotent or it suffices only that the image of the generators to be quas-unipotent?