Thanks for the answer!
But it did not solve the problem.
From ActionScript 1 and 2, I was used to having a code related to the button. Now the code is in a separate layer in the timeline. This is foreign to me and I do not really understand the logic.
Now I have moved the code for the forward buttons to frame 1. The code for the back buttons is still in frame 2. It works, but inconsistently. It works a couple of times and then it stops. Could it be bugs? Maybe I should download the application and Flash Player again?
I doubt it is a bug in the Flash software. I did download your file and I see that if I change the code per what I suggested it does work okay except if you use the "end" button to start things off. Then you get stuck at the end - this is because you skipped the frame where the code gets assigned to the backward moving buttons.
What you might consider doing instead of having the buttons not exist in frames where they won't be used is to instead just turn them invisible in those frames, then turn them visible when you change frames. So in frame 1 you would make the two back buttons invisible and in frame 10 you would make the two forward buttons invisible. Put all of the button event handler code in frame 1 so that everybody is coded up right away and they do not lose it anywhere along the timeline.