Fundamental phenomena occurring in turbulent premixed combustion are investigated via direct numerical simulations (DNS) of two-dimensional vortex-premixed flame interactions. Different strengths Of vortices and fuels are considered in order to analyze the separate effects of strain, preferential diffusion, unsteadiness, and radiative heat losses. One- and two-step chemical models are utilized to study the effect of multistep chemistry, involving an intermediate species, in the flame-vortex interaction. The two-step mechanism consists of a first-order chain branching reaction between reactant A and radical X, A + X --> 2X, and a second-order termination reaction where radicals recombine to form product P, via X + X --> P. Two lean premixed flames (propane- and methane-air) leading to two different Lewis numbers (respectively 1.7 and 0.95) and two Damkohler numbers are investigated. It appears that the Lewis number is a first-order parameter controlling the interaction. For the propane-air flame (Le = 1.7), multistep chemistry effects are negligible and a one-step chemical model is sufficient to well describe the interaction. Unsteady effects are pronounced, especially for the propane-air flame, even for moderate Damkohler numbers. This observation can have a significant impact on the validity of flamelet libraries used in turbulent combustion models based on the flamelet concept. From the present simulations, a transition criteria which separates flamelet and non-flamelet regimes is proposed for propane- and methane-air flames. Radiative heat losses do not play a significant role during the interaction and can be neglected. Most of the conclusions derived from simulations are supported and confirmed by the experimental data obtained in the first part of this study.