CHEMEQ2: A Solver for the Stiff Ordinary Differential Equations of Chemical Kinetics. This report describes and documents the subroutine CHEMEQ2, used to integrate stiff ordinary differential equations arising from reaction kinetics. This is a second generation improvement of CHEMEQ using a new quasi-steady-state predictor-corrector method that is A-stable for linear equations and second-order accurate. A single integration method can now be used for all species, regardless of the timescales of the individual equations. Start-up costs and memory requirements are low, so CHEMEQ2 is ideal for multi-dimensional reacting-flow simulations which require the solution of a process-split, initial-value problem in every computational cell for every global timestep. The algorithm, its implementation, the FORTRAN code, the internal variables and the argument lists are presented, along with several test problem results.