I think it is not so. These verbs do vary in their meanings depending on the tense used. For example He keeps on looking at us.
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TicceHe keeps on looking at us. - (means that he is looking for some period of time and then he is looking away then, again, at us)Thanks Ticce. But I am absolutely sure that "He is keeping on looking at us" is wrong to native ears. You can use "is keeping"
He is keeping on looking at us. (Here it means that he is looking constantly without stopping)
AnonymousBut I am absolutely sure that "He is keeping on looking at us" is wrong to native ears.Don't be so sure))) I have checked it with a native speaker and it was acceptable to his ear.
AnonymousEnglish is my first language. "He is keeping on looking at us" sounds weird to my ears. I advise you to seek a second opinion. I'm certain it's incorrect. English speakers don't use it in this way.Even if it sounds weird it doesn't mean that this is wrong. However, I agree it is a bit unusual.
TicceThe guy I checked it with is from the UK and he said that it was unusual but still acceptable.Thanks for pointing that out. I believe I've used the wrong word, "incorrect" is too harsh. But as the British fellow has told you, it's unusual and we do not normally use this in speech but perhaps in literature where more artful language is used. The a