I'd let the neighbor know there's a problem and ask them how often they feed their cat. Apparently he's found a food source and is hungry enough to find a way to get to it.

Other than keeping your cats indoors, or checking/replacing the cat door, I can't think of any way to keep the visitor out.
Have you tried not leaving any food out while you're gone?

It's not difficult for a cat to figure out a cat door. I've had a number of cats who prefered lifting the door towards them to get out.
Definitely talk to your neighbor. If the neighbor just got a cat, but leaves it out day and night, why have a cat? But that's fodder for a whole other thread.
I agree with Annz about not leaving food out during the day. You may have to keep your cats on a feeding schedule at least temporarily until the intruder figures out there's no chow.

You have two problems.

One is that your cats are going outside unsupervised.

The other is that your neighbors cat is going outside unsupervised.

If you correct these two problems, the cat door will not be an issue.

http://www.purrfectfence.com/

4 indoor/outdoor cats in this house. The only place food is available is INSIDE. And a human has to open the door to access it.

I know it's not going to make your lives easier, but I'd keep the flap "buttoned up" when you're not there to monitor who is "chowing down". I've read some pretty funny stories about wildlife that has shown up a the feed trough at odd hours. My own experience has been that they've brought in live prey items... lol, I found a fully viable Chippie on a pile of laundry some weeks ago, have also dealt with a Blue Jay, a snake, and a vole. Took me 2 hrs. to convince Chippie to go back outdoors.

We feed in the morning, and let them out if they want to go out. When I get home about 2PM they have the option of another snack but rarely avail themselves of it. By 5-7PM they're hungry. When they come in for dinner, they're in for the night. Generally speaking, you can predict their return.

Cats are smart and you can train them. The only thing that is sort of tough here is the changing the clocks... but within a day, they're on to the next schedule. I don't mind being a "doorman". In the long term, it's just easier.

Oh geeze, lets not go here again, you don't know where your cats are going when yours are out nor do the other people that let theirs roam. If you dont keep them confined to your own property, you cant complain about others that dont either. As nicely as I can put it....well I dont need to say, you know. Read the other threads. You are creating the problem and YOU can fix it easily.
Lisa

If your neighbors are leaving this cat outside day and night, are they even feeding him? If he does not have access to food and water at home, he will do what he has to do to survive. Surely, you wouldn't want him to starve?

Alepat, there are many members here who believe cats should be indoors only. I don't happen to agree with them. I have offered my suggestion based on the fact that I allow our cats to go outdoors. Whether or not you decide to restrict your cats to your home is entirely up to you, but if you opt to continue permitting them access to the great outdoors you will likely receive one reply after another telling you how irresponsible/selfish you are.

Just wanted to warn you! ;)

Oh more of the indoor only cat dogma. My cats go in and out, they hunt mice in the barn and they can't do that if they are in the house. Kitty Sheena saved me from getting bit by a rattlesnake this summer, she knew it was in the barn behind the feed buckets I was sticking my hands in and showed me the snake. It was the biggest rattler I ever saw four feet. They don't go to the nieghbors because they live too far. I don't have a flap door because the livingroom will be filled with wood rats and voles lol. I have six cats and they only got one bird, it was a quail we have a flock of about 200 quail that live here. I also don't have a bird feeder but have plenty natural food for birds. The cat might be eating your cat's food, not because it is hungry but because it is another cat's.

Woah, I didn't expect this :)

This isn't really the thread for this but IMO I don't see the point of owning a cat (or dog) and keeping it couped up inside all day. Again I also don't see the point in keeping it outside at all times. I personally find both ways to be unfair to the cats.

@anna & noinwi - I already limit the food I put out but thanks for the suggestion.

@petra - No I don't want the cat to starve (thats how I got my second cat, she was a stray I took in) but then again I don't see the point in paying money to feed a cat that I know has a home.

@chelone - Don't really have problems with snakes, chippies (chipmunks??) & voles in the west of Scotland :) I've had the odd "present" of a small bird in the morning but IMO thats part and parcel of owning cats (it's only ever the stray that brings the "presents" for me. My other cat (which I got from a cat shelter) is not really a hunter.

Again thanks to everyone for the replies

alepat, maybe you can talk to the neighbors and ask if the kitty has access to food/water. If they refuse to let him in to feed him, they should at least leave food and water out for him. A gentle reminder might help push them in the right direction. :o)

I find that a great many people have cat flaps in Europe and the UK. I can honestly say in my cat fostering group and all the animal people I hang with..never saw one in this area. A cat would be the least of my worries because I feed a skunk every night but he lives under my garden house and that 's as close as I want him, cute as he is. And Husband was eating lunch and reading way up in the yard near the pond when something furry rubbed his legs. Since all my cats are indoors only, I have tons of chippies and squirrels everywhere. He looked down w/o moving and thought it was a cat.. not ours but a stray. Turned out it was a woodchuck!!He split as soon as he realized that this thing he rubbed was attached to a human! I just wouldn't want any of my creatures to get into my kitchen..