I have often found authors to make the mistake of being confused between “something undergoing” and “something under way,” even authors who otherwise have produced a well-written output. An example sentence:

This crisis has been undergoing since the start of the present century.

Change to

This crisis has been under way since the start of the present century.

In a short sentence like the above example, this is easy to catch, but in longer sentences, you may miss it, since both “undergo” and “under way” are not that far off semantically: both imply a certain kind of motion, a process. (In the case of “undergo,” it is the unpleasantness (often, but not always), the transition, the inflicting that is in focus, with the continuity not really in question, whereas “under way” is more about a process that lasted for a certain duration, and it is this interval that is in focus.) It is rather important to remember that “undergo” can only be a transitive verb (so someone or something has to undergo something), just “undergoing” with no object taken is not fine. For example, a country can undergo a crisis, but during that time the crisis is under way (and remember, the adverb should be two words, not one word, viz. “underway,” which is only used in adjectival usages).