Is the Homeworld series compatible with Windows 7 x64?

I remember I greatly enjoyed the Homeworld series back in the early 2000s, and would like to play the games again.

Homeworld
Homeworld: Cataclysm
Homeworld 2

However, I'm concerned that they may not be compatible with my newer computer. Do these games work well under Windows 7 64-bit, or are there significant compatibility issues? Are there any workarounds to enable compatibility, which I should be generally aware of?

I'm looking to have some assurance to compatibility prior to re-purchasing the games.