Is it normal for a guy to take days to respond to a text?

The delay on its own is ambiguous, so look at the shape of his reply. If he answered with a full sentence, asked you something back, or referred to something specific you said, the wait was almost certainly about his schedule. A one-word answer with no question attached is a different signal, and so is a reply that ignores the thing you asked. Pay attention to whether he apologized or just answered. People who care about the thread often mention the delay themselves, even briefly. People who do not care usually just answer and move on without acknowledging it.

His profile and the stage you are at also count. Early on, a three day gap after a good first date can mean he is not sure what he wants, or he is juggling other conversations. Later, after you have made plans, the same gap is more likely to be ordinary busyness. Neither reading is certain, so use the pattern across several messages instead of one slow reply.

When you reply, your job is to make it simple for him to answer, not to reopen the question of the delay. Aim for a message that is short, warm, and asks for something specific he can answer quickly, like a choice between two plans or a detail about something he mentioned. Matching his length is a good default, since a long message after a short one can read as pressure. Keep the tone light and let it be clear you are not keeping score.

Avoid anything that makes him account for the silence. A message that moves forward on what you were already talking about does more than one that asks why he went quiet. If he has been giving short answers, one clean follow-up question is enough. Do not stack several messages in a row. Let the thread breathe, and let his next reply decide what happens.

Send your first follow-up after a reasonable gap, often a day or so after his last message, and treat that as your move. If he replies in a way that carries the conversation forward, keep going and match his pace. If he does not answer, wait a few days before anything else, and do not send a second nudge in the same afternoon. One gentle check in after a longer silence is fine, since people do lose threads by accident.

If the second stretch also goes quiet, or he answers each time with the same low effort, stop sending. You have given him two clear chances to show up and the signal is consistent. Keeping the thread alive with more messages usually just keeps you waiting. Let it end without a dramatic message, and put the energy into people who reply at a pace you can build on.