The blue and yellow squares move exactly in step.  But when the background is striped they seem to speed up and slow down in alternation.  Reason:  when the leading & trailing edges of the dark blue square lie on the black stripes, their contrast is low so the motion looks slower (Pete Thompson 1976).  On the white stripes the edges have high contrast so the motion seems to speed up.  The opposite is true for the light yellow squares.  Maybe this is like cars that appear to go slower in the fog.

Fixate on the red cross. The squares appear to wiggle in and out toward and way from each other.

Reason: As the dark square hits a white vertical line and its horizontal motion speeds up, it also hits a black horizontal line and its vertical motion slows down. For the dark square, the top and bottom edges have high contrast, the left and right edges have low contrast, and so its vertical motion is exaggerated. For the light square, the opposite is true.