  We will announce two theorems. The first theorem will classify all
topological types of degenerate fibers appearing in one-parameter families of
Riemann surfaces, in terms of ``pseudoperiodic'' surface homeomorphisms. The
second theorem will give a complete set of conjugacy invariants for the mapping
classes of such homeomorphisms. This latter result implies that Nielsen's set
of invariants [{\it Surface transformation classes of algebraically finite
type}, Collected Papers 2, Birkh\"auser (1986)] is not complete.
