These conjunctions come in pairs. We have five of them:
not … but not only … but also both … and neither … nor either … or
All good writers routinely use these conjunctions in their style. You should, too.
When you do, make certain that the two parts of the correlative conjunction join two grammatically equal elements. If the first part joins an adjective, then the second part must join an adjective. Thus, it would be incorrect to write: He is neither my friend nor happy. You cannot join a noun (friend) with an adjective (happy).
Also, when you use neither … nor to join two subjects in a sentence, the number of the noun closer to the verb governs the number of the verb. Study the following two examples:
Neither the player nor the coach wants to lose. Neither the coach nor the players want to lose.