Can you cast an instant during your opponent's end step after they pass priority?

During any phase or step, each player receives priority in turn order. In your opponent's end step, your opponent first receives priority (CR 116.3b). If they pass priority without taking any action, priority passes to you (CR 116.3d). At that point, you may cast instants, activate abilities, or take any action that is legal at instant speed.

The end step is still a step within the turn, and instant-speed actions are explicitly allowed outside of your own turn (CR 116.1, 307.1). There is no restriction that prevents you from acting during an opponent's end step — in fact, this timing is commonly exploited by experienced players precisely because it is the last moment before the opponent's turn ends and they untap.

Note that if both players pass priority in succession without anyone taking an action, the current step ends (CR 116.4). So if your opponent passes and you also pass without acting, the game moves to the cleanup step, where you normally cannot cast spells unless a triggered ability goes on the stack.

Example: It is your opponent's end step and they tap out for a spell, then pass priority. You respond by casting Doom Blade targeting their creature. This is a legal instant-speed action taken during their end step after receiving priority.

This timing window is important for cards like Snapcaster Mage or end-of-turn draw spells, allowing you to use your mana efficiently without giving your opponent another chance to respond before their turn ends.