In this report, we have shown that the numerical method of lines can be used effectively to solve time-dependent combustion models in one spatial dimension. By the numerical method of lines (NMOL), we mean the reduction of a system of partial differential equations to a system of ordinary differential equations (ODE's), followed by the solution of this ODE system with an appropriate ODE solver. We used finite differences for the spatial discretization and a variat of the GEAR package for the ODE's. We have presented various solution methods of interest for the nonlinear algebraic system in this setting; that is, in the corrector iteration section of the GEAR package applied to combustion models. These methods include Newton/block SOR (SOR denotes successive over-relaxation), block SOR/Newton, Newton/block-diagonal Jacobian, Newton/kinetics-only Jacobian, and Newton/block symmetric SOR. These methods have in common their lack of frequent use in ODE software and their ready applicability to partial differential equations in more than one spatial dimension. Finally, we have given the resutls of numerical tests, run on the CDC-7600 and Cray-1 computers. By so doing, we indicate the more promising nonlinear system solvers for the NMOL solutionof combustion models. Specifically, our purposes are to: demonstrate the feasibility and accuracy of the numerical method of lines, in comparison with a splitting scheme,for a one-dimensional combustion model; discuss various approaches to the problem of solving the algebraic systems that arise from implicit methods; and show that the numerical methods described here are applicable to multidimensional problems and ot other transport models.