For some years now a black tomcat has been coming in through my catflap, hoping to steal some of my little female cat's food I suppose. I always assumed it belonged to a neighbour. However, recently people have commented that it is feral. GS got a good look at it the other day and it is moth-eaten and looks like it doesn't have a proper home.
At first, if the cat was in the kitchen and heard one of us walking about it would hurl back out through the catflap. You only ever saw a disappearing black tail More recently, however, it has grown progressively bolder and just strolls out.
Last night, I went into the hall to see the cat was in. It sauntered into the kitchen and paused at the catflap looking over its shoulder at me. I did the usual soft voiced chat to it and moved closer. I intended to give it something to eat but it exited just before I got there.
So I put a saucer of cat food on the back step and called the cat (I have named it Blackie). To my surprise it miaowed from under my car just by the back door. It came out and ate the food right in front of me. So I fetched a few cat biscuits and put them in the saucer. The cat swiped at me with his paw (claws in). Like lions do to their trainers 
I probably have not done a wise thing in making the cat feel welcome. It's likely it has fleas and I can't see it would ever be tame enough for me to take it to a vet to be checked over. Also, I have always thought of the cat as slightly sinister but it intrigues me and it is, after all, one of God's creatures.
Cat lover, what do you think I should do next?