  We consider the following generalization of the decomposition theorem for
polycycles. A {\em $(R,q)$-polycycle} is, roughly, a plane graph, whose faces,
besides some disjoint {\em holes}, are $i$-gons, $i \in R$, and whose vertices,
outside of holes, are $q$-valent. Such polycycle is called {\em elliptic}, {\em
parabolic} or {\em hyperbolic} if $\frac{1}{q} + \frac{1}{r} - {1/2}$ (where
$r={max_{i \in R}i}$) is positive, zero or negative, respectively.
  An edge on the boundary of a hole in such polycycle is called {\em open} if
both its end-vertices have degree less than $q$. We enumerate all elliptic {\em
elementary} polycycles, i.e. those that any elliptic $(R,q)$-polycycle can be
obtained from them by agglomeration along some open edges.
