3 answers
At the beginning of a sentence, "nesmotrya na" (despite/notwithstanding) typically requires a comma after it. That is, the correct way to write it is: "Nesmotrya na ustalost, my prodolzhili put" (Despite the fatigue, we continued on our way). The preposition with its dependent word forms a parenthetical phrase that is set off by a comma - this is not a matter of style, but a rule of punctuation.
The tricky part is that many people confuse this with ordinary prepositional constructions without a parenthetical phrase. If we wrote simply "Nesmotrya ustalost" (without the preposition before the noun), that would be a participle and would require a comma for a different reason. But "nesmotrya na" is exactly a preposition, and a prepositional construction at the beginning of a phrase is set off by a comma because it separates the main clause.
Exception: if the phrase is very short and flows easily without a pause, sometimes in literary texts you'll see it written without a comma. But strictly speaking, this is a deviation from the norm, not a rule. Go with the comma - you won't make a mistake.
No, you don't need a comma. "Nesmotrya na" at the beginning of a sentence is a preposition with a dependent word, and it doesn't require punctuation. You'd only need a comma if it's a participial phrase ("nesmotrya na ustalost, ona prodolzhala rabotat") or if there's a clarification after it. In the general case, you just write: "Nesmotrya na plohuyu pogodu, my poshli gulyat" - the comma here separates the phrase from the main clause, but "nesmotrya na" itself doesn't get one.
You need to distinguish between two different cases, and the previous answer kind of mixed them up. When "nesmotrya na" stands at the beginning of a sentence and introduces a phrase with its own complement (like "Nesmotrya na ustalost, my poshli dalshe"), a comma is indeed not required - it's just a prepositional phrase, nothing special. But if "nesmotrya na" opens a full subordinate clause or stands between two independent parts, then a comma might be needed to separate the semantic parts.
The simplest rule works like this: use a comma only if you feel that after the introductory phrase a new, independent part of speech begins - the main part of the main sentence. For example, "Nesmotrya na plohuyu pogodu, match sostoyalsya" - here a comma makes sense because it separates the concessive phrase and the main clause. And in a construction like "Nesmotrya na vse prepyatstviya my doshli do tseli" a comma is also possible, but its absence won't be an error if the meaning stays clear.
Basically, at the beginning of a sentence it all depends on the intonation and how you want to place the semantic emphasis. There's no hard rule.
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