Strategies for assembly and analysis of human, yeast, and bacterial RNA polymerase elongation complexes are described, and methods are shown for millisecond phase kinetic analyses of elongation using rapid chemical quench flow. Human, yeast, and bacterial RNA polymerases function very similarly in NTP-Mg2+ commitment and phosphodiester bond formation. A "running start, two-bond, double-quench" protocol is described and its advantages discussed. These studies provide information about stable NTP-Mg2+ loading, phosphodiester bond synthesis, the processive transition between bonds, and sequence-specific effects on transcription elongation dynamics.