In this work, a comprehensive study of flamelet tabulation methods for pulverized coal combustion in a turbulent mixing layer is conducted. At first, a priori analyses are conducted to evaluate the suitability of the premixed and non-premixed flamelet models for the studied pulverized coal flame with multiple combustion modes. Then, to clarify why a certain flamelet model does work or not work in certain regions, a more in-depth investigation of the premixed and non-premixed flamelet models is conducted through a budget analysis. The results show that the first and second derivatives in physical space can be well reproduced by the tabulated manifolds in trajectory variable space for both the premixed and non-premixed flamelet models, between which the non-premixed flamelet model performs slightly better. For the time derivative, large discrepancies can be observed, although the predicted variation trend overall follows the reference results. Through the analysis of the individual budget terms in the trajectory variable space, the individual trajectory variable's contributions to the convection and diffusion of thermo-chemical variables are quantified. Through the analysis of the individual budget terms for the sensible enthalpy and the CO mass fraction governing equations, the influences of the space transformation on the individual transport process (e.g., convection, diffusion, etc.) are clarified. Overall, the findings obtained from the budget analyses are consistent with those obtained from the a priori analyses. (C) 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.