Next door's cat in my garden

[Itwasaquarterpast11]

We moved in 6 weeks ago. She has finally, this evening, after 6 weeks of prowling along the fence and sitting on my roof, decided to come into my garden. I naively thought this was because she found my two 6 month old kittens irresistible and wanted playmates. Nope. She has hissed at them, stalked them and chased them.
My boy cat is petrified and climbed me like a tree. My girl cat is a bit dim and just rolled around in the grass, oblivious.

I felt like an anxious mum on a failing play date. I don't want to piss my new neighbours off, but I don't want my soppy pair to get eaten by the (very dainty, but very mean) girl next door.
Previous cat was indoor (by choice) so this is new territory for me. Any advice, please?!

Ill probably get flamed but I'd give it a squirt with a water pistol every time it comes into the garden and displays aggressive behaviour to your cats ... it'll soon learn not to bother

They'll work it out between themselves - no matter how hard you try to police it. They will work out the pecking order between them. My cat's an outdoor cat and big too. Plenty of other cats wander though what you would have though of as 'her territory' - our garden. Some get hissed art, some get totally ignored, some are treated with wary respect and kept away from. I have no idea why cats smaller than her are treated with caution and other bigger cats run away from her on sight. Cats are weird animals.

Keep an eye out but let them sort it.

Thank you both. I spent ages hovering anxiously, so clearly my approach was fairly pathetic! The advice and explanation are appreciated.

Hissing is totally natural and ok. They're on her turf after all. They'll work it out. Cats don't tend to full on fight unless they are un-neutered. We've recently had a 12 week old kitten and i have a very big, extremely friendly ginger tom. He hissed and batted her off for days. Fast forward 3 weeks and they're best mates. My old black cat seems to quite enjoy the peace now my ginger Tom is occupied.