I have a quite simple animation, a text in a big font moving continuously (pixel by pixel) to the left. The text is first converted to an image, then a timer task is started
Try calling this method when you are done drawing:
Toolkit.getDefaultToolkit().sync();
This flushs the graphics buffer which some systems like Linux use. See the Javadoc: http://docs.oracle.com/javase/7/docs/api/java/awt/Toolkit.html#sync()