  In this paper I continue the study of iterated integrals of modular forms and
noncommutative modular symbols for $\Gamma \subset SL(2,\bold{Z})$ started in
[Ma3]. Main new results involve a description of the iterated Shimura
cohomology and the image of the iterated Shimura cocycle class inside it. The
concluding section of the paper contains a concise review of the classical
modular symbols for SL(2) and a discussion of open problems.
