As a generalization of part of a work of Dubrovin, we introduce for any simple Lie algebra an infinite family of pairwise commuting ODEs and define their tau-functions. These ODEs have a Poisson structure obtained from the r-matrix theory. We show that the tau-functions can be identified with tau-functions for the corresponding Drinfeld--Sokolov hierarchy. Geometric aspects about the ODE system will be considered. The talk is based on a joint work with Cheng Zhang and Zejun Zhou.