2 lousy anime films

[The Fake Macoy]

I vaguely recall 2 animes that I saw part of (they seemed pretty lousy) on TV.  I believe I saw them in the late 90s or early 00s.  They were playing on the Space channel (in Canada), I believe on a Saturday afternoon.  They looked like they were from the 80s, but I could be wrong.  Both films looked like they were set in the present day or maybe a sci-fi future scenario.

Film 1:  The Cat one
This one I'm not sure if it was dubbed or not.  I think it may have been subtitled rather than dubbed.  What I remember is that there was a group of people, I think they were a military group.  It looked like the main character (a woman) was in a coma and having a flashback to another event.  In the flashback she was fighting a giant cat and people from her team/unit helped her.  She then woke up and talked to her team about it.

Film 2:  The super-powered one
This one was dubbed into English.  I think the main character had green hair.  He was talking to some girl who told her that when she was a child, some bad guy and his goons broke into her house and I think killed her parents, then beat up her and her brother.  In the present time the brother was now trying to find this bad guy and kill him.  Somehow, during a battle, the brother got confused and I think stabbed his sister with a sword.  He realized what he had done and later cried tears of blood.  I believe there was a scene where some of the bad guys, who could fly, went to attack someone.  The hero flew/teleported into the sky to confront them, and they said he was too tough and had to run away.  I seem to recall there was some narration during some scenes.

I know this is all very vague.  I only a few minutes of them, probably when I was flipping through channels looking for something to watch.  These were probably both the types of crappy anime that was brought over in the 90s.

[retrorussell]

That first one sound like maybe LILY C.A.T..
http://www.youtube.com/watch?v=sU08-wEBouo

[The Fake Macoy]

Thanks for the reply, but that isn't it.  I think the one I was thinking of was set in a desert, or at least their big battle was, rather than in space.  I realize my description is pretty vague, but I'm afraid I don't really remember much.