badlogic :Could you please try your example without the Mali Texture Compression? I'm afraid I'm currently away from my development machine, so I can't test myself.
The original image files are in ktx format, not png. I haven't found any other programs that can convert ktx to png, so I can't do without the Mali Texture.
Perhaps you can tell us the best converter .ktx->.png?
I'm sorry if my tone of response seems bad. My English is bad.
I found a solution to the problem. The problem was in Mali Texture. The program has crookedly converted files.
Now I use PicoPixel to convert ktx to tga, and from tga many converters to png. Now the animations are played back as they were meant to be!
@badlogic, thank you so much for the tip, you were right!