Nope cards aren't played on your own turn.
You can play a Nope card at any time before an action has begun, even if it’s not your turn
You play them as a reaction to the card whose effect you want to nullify before it takes effect.
Stop any action except for an Exploding Kitten or a Defuse card.
- Player A plays an Attack card.
- The Attack cards takes effect (ending their turn and giving Player B two turns).
- Player B plays an Attack card.
- The Attack cards takes effect (ending their turns and giving Player C four turns).
- Player C plays an Attack card.
- Player D plays a Nope card.
- The Nope card takes effect (canceling the Attack card)
Because the Attack card had no effect, it's still Player C's turn. In fact, Player C has three other turns after this one (because of Player A's and Player B's attacks).
Note the original ("nerfed version" of the) rules did not have chained Attacks carry forth extra turns, so C would only have one extra turn rather than three.