Two operator-split schemes designed for handling stiff chemistry are proposed within a dual-time framework and tested using zero- and one-dimensional test problems. Both are shown to perform robustly without ad hoc time-step restrictions. The first scheme is a Physical Splitting Scheme that is a straightforward extension of the Strang splitting method. Like the Strang splitting method, it retains the issue of splitting errors degrading solution accuracy at large time steps. However, it performs well at small time steps and remains competitive because the scheme involves only two ODE solutions per physical time step. The second scheme is the Consistent Splitting Scheme that is designed to eliminate the splitting errors, but is relatively more expensive because it requires two ODE solutions per pseudo-time step. This scheme also performs well at small to moderate time steps, but its accuracy also degrades at large time steps in part because of issues associated with finite precision. This study indicates the relative strengths and weaknesses of operator splitting approaches and points the way for continued research. (C) 2018 The Combustion Institute. Published by Elsevier Inc. All rights reserved.