[@HPTT2], [@Ko1], [@Ko2], [@Ko3], and [@Ko]. We will prove the following:

\[thm:realmain\] Any hyperpolar action of a compact connected Lie group on a symmetric space of compact type is Cohen-Macaulay.

The proof relies essentially on the classification of the actions mentioned in the theorem, which was obtained by A. Kollross in [@Ko]. Before stating this result, we need to describe an important class of examples of hyperpolar actions on the symmetric space $G/H$ mentioned above. Let $\tau$ be another involutive automorphism of $G$ and consider its fixed point set, $G^\tau$, along with the identity component $K:=G^\tau_0$. The action of $K$ on $G/H$ by left translations turns out to be hyperpolar, see [@HPTT1 Ex. 3.1]. It is known under the generic name of a [*Hermann action*]{}, after R. Hermann, who first investigated this situation in [@Her] (note that originally, in [@Her], the group $G^\tau$ was assumed to be connected). According to Kollross’ theorem [@Ko], any hyperpolar action is orbit equivalent to a direct product of actions of one of the following types: transitive, of cohomogeneity one, or Hermann (for the notion of orbit equivalence, see Sect. \[oea\]). We already know that any action of one of the first two types is 