First: Are you in war or have you a non-aggressive treat with the AI? Both enables them to move into your influence. As you have conquered the city, I expect that you are at war with them.

Secondly, in the City details screen, there should be an option to raze the city or?

Br

Wyl

@Wylaryzel - Yeah, we were at war. But even when you're at war with someone, I don't think you should be able to set up new cities in their area of influence. I expected a 'raze city' option somewhere in the city details screen, but I couldn't find one.

@hermes33 - I know I'll still get the resources, but I won't get the extra bonuses from the fancy buildings in my big city if the resources are closest to this new outpost will I? Cheers for the info about razing needing a technology. I assume that's a warfare tech. I sure hope you can raze your own cities, or I'll have to do something odd like wait for the outpost to be captured before recapturing it again and razing it this time.

@dragoskani - That worked great, thanks! A case of RTFM I guess. But I wasn't sure if the manual would actually be accurate, so that's why I didn't turn there first.

I'm not sure that you do. I didn't have that tech, I just used X after I captured it. Perhaps that's also a bug? I didn't get an option to raze it as I captured it, but that obviously doesn't matter when you can just remove it after you capture it.