If "country property" = 5 acres or 20 acres or somesuch, and you have a neighbor, ya have to expect his cat(s) to wander a few dozen or a few hundred feet. If "country property" = a section or two and the neighbor is a couple miles off, then the cat(s) may well be feral and not a family pet. We've all read about things like this escalating into nasty physical fueds and court battles, so be careful.
Cats are welcome here, however...
I've perpetually had problems over the years with townfolk buying subdivided "ranchettes" consisting of 5 or 10 acres a couple miles or so away from me, then letting their dogs run loose, because, after all, they're in "the country" now. Dogs like to pack up and chase wildlife and domestic livestock, but when I confront these people about it, the answer is invariably, "Our dog never leaves our yard". Many times, I've found newborn calves all torn to hell from these nice, well behaved doggies, so quite often they never leave my yard.
Ya do whatcha gotta do, then follow the 3S rule: Shoot, Shovel, and Shutup.