  Given our set-up of a system of curves and maps between them satisfying
certain assumptions, we prove a classicality criterion for overconvergent
sections of line bundles over these curves. As a result, we prove such criteria
for overconvergent modular forms over various Shimura curves. In particular, we
provide a classicality criterion for overconvergent modular forms studied in
[Kassaei: P-adic modular forms over Shimura curves over totally real fields,
Compositio Math. 140 (2004), no 2, 359-395] and their higher-level
generalizations.
