means "before long" or "eventually": time passes and something comes about as the natural next step. It is an adverb, so it takes no particle and goes at the head of the clause or just before the predicate. It belongs to writing and storytelling; in conversation
or
does the same job.
。
Before long, the rain stopped.
。
The two of them eventually got married.
。
That small company eventually became a global corporation.
About the future, it predicts what time will bring, usually with or a plain non-past.
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Spring will come before long.
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Children grow up in time.
Before a length of time, やがて means "nearly": the amount is about to be reached.
、。
It's coming up to three years since I came to Japan.
やがて, もうすぐ and ついに
says something is very close, as if you were counting down to it. やがて only says it comes after a while, without saying how close.
adds that it comes at last, after a long wait or a lot of effort.
。
The train will be here any minute.
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Even the long war came to an end in time.
、。
After ten years, it was finally finished.
やがて describes what happens on its own, so it does not go with a request.