Please help. I have two cats and need help. One is a stray...?

I found a stray cat that is a male, and took it home because it was starting to sleet outside. So, we have a female cat at home that's about 9 years old... The stray cat we got is about... 3 years about. We get home and the stray sniffs around. It's been 1 day since we've had him, and my female cat keeps hissing at him. Our stray cat just meows and wags his tail (like a rattlesnake...) and tries to be friends I THINK? Can you tell me if my female cat is just being territorial or does not like the male cat?