Hey newt, thanks for Your quick reply!
I think You misunderstood my problem. In fact the animation plays fine this way, although I see that Your code should actually be the right one when I think about it? lol; I mean it doesn't keep displaying the first frame of animation with my code, it plays normally and loops.
Anyway, my problem was not with the display of the animation, but the correct movement in time, relative to the animations original fps. It was animated to be seen with 16fps.
That means, the sprite should only move forward in X, when it changes frames to the next frame in its loop.
Now the application itself is set to run with V-Sync.
The animation itself in its "animators properties" area is set to run with 16fps.
So, as long as the Thumbstick is held in the forward direction, the walking animation will be playing, it will play with it's own fps set in the animator and should be move forward in X, every time the frame changes.