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My paper is undergoing its third revision in a journal, primarily focusing on applied mathematics. There are some technical parts in it, but nothing really out of reach.

The time line is something like this:

-Submission to the journal.

-Eight months wait for the reports. Reviewers provide in-depth and crucial feedback. Both reviewers express difficulty delving into details due to writing issues, a point with which I agree. The paper, particularly given my non-native English background, was poorly written, and I was not aware of Grammarly and AI tools at that time. Still, there was many other important in-depth remarks about the model. In particular, I was required to provide with some comparisons with other tools in the field.

-Resubmission (1st major revision).

  • Eight months wait for the reports. One reviewer sent his report quickly, but I had to wait both reports to be sent to read it. This one has only minor remarks but expresses its satisfaction overall; he finds my comparisons interesting and is fine with the paper as such. The other one, who seem to be a native speaker, finds the paper better, but still challenging to read and poorly written. At this stage, I am in a situation where I do not want to make too many changes, fearing to touch to something that the first referee liked. Still, I manage to clarify the paper further by incorporating mathematical results, initially in appendices, into the main text, and I broke down fundamental notions into smaller pieces. Now I believe there is a significant improvement in the way to convey the insight.

-Resubmission (2nd major revision). -Eight months wait for the reports. The first referee expresses that he is satisfied. But now the other one is focusing only on LaTeX remarks and notational criticisms, maintaining that the core part of my paper is "incredibly technical" (come on...), too technical to delve into. I now start thinking this is an exaggeration and potentially procrastination. There's a lengthy list of recommendations for minor LaTeX adjustments and criticisms of my notational choices. But at this stage, trading a notation for another one is just trading one inconvenience for another one... The paper is now quite stable, and though I took into account some interesting notational shortcuts, this new version is not fundamentally different from the previous one.

-Resubmission (3rd major revision).

-Now I have been waiting for another four months. Nothing moved since then. I see that the first referee submitted his report in a few days (probably saying one more time that he is satisfied, at least I hope), but and am growing increasingly frustrated about the inactivity of the second reviewer. It has been over two years since the initial submission. The editor is very professional, friendly and responsible. He perfectly understands the problem, but he cannot do more than nudging the reviewer. Should I approach the editor once more? Last time I contacted him was six or seven weeks ago.

I apologize for posing a question that has likely been asked many times, but the extended waiting period seems unusual.

Thank you in advance for your suggestions !

BNPO
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    Is it a Q1 journal? Would you consider sending it to a different journal? – AkiPhD Nov 28 '23 at 09:57
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    “I was not aware of Grammarly and AI tools at that time.” You could also just send it to a colleague who’s confortable with English. –  Nov 28 '23 at 11:25
  • https://academia.stackexchange.com/questions/88355/is-my-paper-under-review-or-similar-for-too-long-and-if-yes-how-should-i-reac Does this answer your question? – Allure Nov 28 '23 at 11:26
  • As for waiting 8 months for a review, if you accepted to wait that long the first 2 times, why not this time? Personally I’d write to the editor after about 2 months of waiting for reviews, and probably retract the submission after 3, but it’s maybe field-dependent. –  Nov 28 '23 at 11:28
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    "but he cannot do more than nudging the reviewer." Yes he can. He can nominate a new reviewer and discard the one that doesn't do their job if the new reviewer sends a report earlier. He can even in principle make a decision based on one review and his own reading, if he feels comfortable about that. – Christian Hennig Nov 28 '23 at 11:53
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    @leonos I don't think three months is very unusual in applied math. This easily happens if some reviewers decline and somebody who promises a review doesn't send it. Two years is unusual though and hard to justify. – Christian Hennig Nov 28 '23 at 11:55
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    Thank you a lot to you all for your answers, this helps me figuring out the situation better. Yes it is a Q1 journal. Three months is normal for applied maths. It is normal that we need time to get familiarised with the model. I am not too shocked that we need eight months, even though I personally think that six months is a maximum. What is unusual is that we need this amount of time between each resubmission. – BNPO Nov 28 '23 at 13:59
  • Actually, I remember suggesting finding new referees in one of my letters to the editor, or proposing new referees myself. But apparently, he wanted to keep these ones. – BNPO Nov 28 '23 at 14:07
  • @BNPO I would find such a suggestion a little bit unprofessional, to be honest. However, I understand you. – Jan Nov 28 '23 at 20:35
  • I did not insist too much on that, and I understand that the editor prefers to keep the initial reviewer. As Jan is saying, the editor understands my problem. I do not think proposing new reviewers is that unprofessional, in general, since editors who are not familiar with the model need ideas about who contacting. My idea was also something like "maybe we need someone else who can delve into the details, so that the editor will have more cards in hand to appreciate the paper". (I wrote "these ones", but I meant "this one") – BNPO Nov 29 '23 at 08:45

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Waiting 1-2 years, even for the first revision, is not unusual. I understand your impatience and frustration, but you cannot do much now. Writing to the editor is OK after some time; journals usually say one year. In this particular case, I do not think it is a good idea to write to him once again. As you say, he understands you. On the other hand, he cannot push the referee too much. In the end, for the referee, it is a voluntary work. The system is clearly far from ideal at this point, but for now you have to cope with it.

Jan
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