Axis-Angle Transformations

I posted this question before, but I constructed it in the wrong way, which misleaded a lot of people. I''ll try to rephrase it so it will be easier to understand. I define an orientation of a model in the world using a vector and an angle around it (angle-axis). I am applying vector-angle transformation v1 to the model. Then I am applying a different vector-angle transformation v2 to the model. Is there a way for me to get v1 and v2 combined, meaning the new angle-axes of this model? The opengl anology of this is the following: glRotate(v2.a, v2.x, v2.y, v2.z); glRotate(v1.a, v1.x, v1.y, v1.z); How do I get v3, the result of the previous two transformations? Thanks.