There is an article which contains a section describing preliminary materials, that is, results which have already been published elsewhere and on which the current work is based.
This section is not supposed to contain any new result.
It appears that part of this section (one to two pages) is, up to minor modifications, a copy-paste from another published article.
The other article is from a collaboration of the author of the present paper with other authors. It is cited somewhere in the current article but not as the source of the copied part.
The context and methods of the articles are very similar (hence the need for similar tools), but beside the copied part, the contents and results are different.
In particular, there does not seem to be any plagiarism in the actual novel part of the article in question.
Is this a case of acceptable self-plagiarism?
There are a lot of questions in academia.SE about self-plagiarism but I couldn't make my mind about this case from what I've read.
EDIT: Thank you for all this helpful contributions. As referee for this article, I've chosen the option to ask directly the editor's opinion.
Lots of people would object to this. LOTS. I think somewhat differently. If this section doesn't cite the original, I think that's pretty bad. I don't think that it's career-ending, but I also don't think that we should be slavish to not copying ourselves when the material is rote or nearly so. Methodology sections that don't change much from paper to paper are places where I think reproducing text and saying so and citing yourself are particularly acceptable to me, but lots of people disagree vehemently with me. I'm aware of this propensity, so I don't copy text in my own papers as much as possible. I rewrite such sections and cite my old work for alternative descriptions.
In the case you mention, both articles appear to have been published, so unless you have a vendetta with this author and want to try to ruin their career, it's probably not worth saying anything to anyone about it. In other words, what would you do if we all said it was bad self-plagiarism? The only thing you can really do is tell the journal or their department chair and hope for a retraction or firing. If it doesn't change the result, then there's not much point in bringing it up. That being said, it's probably best if you don't follow their example. It's also probably worth being wary of future articles from this group of authors since there might be other aspects that aren't exactly above board.