Constraint Programming (CP) allows to modelize and solve combinatory problems by specifying some partial information on variables, unknowns of the problem.We have studied musical constraint problems, either stated by contemporary composers, or of musical analysis, or instrumentation, in collaboration with IRCAM. Fourteen such problems have been modelized and solved, which allowed to give a detailed typology. This has been used to conceive and implement OMClouds, a library in the Computer Assisted Composition environment OpenMusic. It is based on a local search algorithm called adaptive search. Its architecture allows in particular to define a constraint problem visually, to solve it, and eventually to edit partial or approached results during the resolution process.