  Graphs that are critical (minimal excluded minors) for embeddability in
surfaces are studied. In Part I, it was shown that graphs that are critical for
embeddings into surfaces of Euler genus $k$ or for embeddings into
nonorientable surface of genus $k$ are built from 3-connected components,
called hoppers and cascades. In Part II, all cascades for Euler genus 2 are
classified. As a consequence, the complete list of obstructions of connectivity
2 for embedding graphs into the Klein bottle is obtained.
