How do I rotate an object but keep it's direction

My object is moving left/right - when I rotate it around the Z axis it starts to loop around and stay in the same spot. I want the movement on the X axis to not be affected by the Z axis rotation.

How can I do this thanks?

try to toggle from local to world!

Thanks I was rotating the object in Space.World but not translating it in Space.World!

Cheers :).