We present a generalized Langevin equation for the dynamics of semiflexible polymer chains of finite size in a dynamically heterogeneous fluid. Local and global dynamical properties, calculated in the framework of this approach, display anomalous behavior in agreement with experiments and computer simulations. The presence of heterogeneous dynamics induces non-Fickian center-of-mass diffusion and an anomalous slowdown of intramolecular modes of motion. Intermolecular interactions mostly perturb lowest-index modes, which correspond to polymer global dynamics. Internal polymer stiffness induces anomalies in the relaxation of highest-index modes, which characterize local dynamics and monomer diffusion. (C) 2003 American Institute of Physics.