IPhone receives messages hours after they were sent?

Hi, I have a contact on my iPhone and sometimes when he'll send a message, I won't get it until hours after he sent it. He's even shown me that he sent it, but I'll show him that I never received it. Then, around five hours later, I will finally receive his message.
What is going on here? How can I fix it so that I receive all his messages at the time he sent them? It has become a lot more frequent these past few days. It's frustrating because at first he thought I was ignoring him, when actually I never received his messages. It only happens to this particular contact; I have no problem receiving messages on time from other people. He also has an iPhone if that info helps at all. Help me!

Thanks.

Added (1). Is it something that's wrong with his phone or my phone?

One of you probably don't have any service

I don't think your guys iphone is broken i think he might have sending problems or he's cellular data is off and he don't have Wi-Fi and when he turned it on thats when he got your messages. You know even if its an iPhone they still can't receive messages unless the cellular data or the Wi-Fi is on.