Correlated internal dynamics of proteins, which is believed to be important for their function, is analyzed at unprecedented precision using explicit-solvent submicrosecond molecular dynamics simulations of ubiquitin and calbindin D-9k. Without exception, all of the mobile dihedral angle pairs in ubiquitin with sizable dynamics correlations (R-2 >= 0.1) are at short-range distance. In rare cases, they involve sequentially remote dihedral angles that form sparse clusters, suggesting a structural-dynamic propagation mechanism via soft torsional couplings that act over short distances with a rapid loss of coherence over longer distances.