The present work deals with autoignition of non-premixed turbulent mixtures. The objective is to study the possible role that partially premixed combustion may play in the propagation of ignition. First, a physical picture based on simple considerations and describing the structure of the flame very early after ignition is discussed. Then, direct numerical simulation is used to estimate the importance of the role that triple flamelets may play in ignition processes. To focus on the properties of the flame at ignition, and to evaluate the validity of the proposed picture, computations are performed of laminar and turbulent non-premixed mixtures undergoing a compression. In laminar cases; uniform or nonuniform distributions of the mixture fraction gradient along the stoichiometric line lead to two different types of ignition. Uniform mixture fraction gradient brings ignition through an initial premixed system evolving to reaction zones forming a three-layer system, with partially premixed flames developing in the direction parallel to the stoichiometric line. Triple flamelets propagating along the stoichiometric line, are observed, however, for nonuniform distributions of the mixture fraction gradient. Turbulent simulations suggest that both of these partially premixed fronts are likely to be observed in a turbulent environment. The time evolution of the mean amount of heat released allows for distinguishing between these ignition regimes. The appearance of a single peak during ignition is an indicator of regimes corresponding to either combustion in a three-layer system or combustion in which triple flamelets are dominant at the very beginning of ignition. When two peaks are observed, ignition first occurs in a premixed regime (first peak), and then triple flamelets propagate ignition (second peak). It is concluded that partially premixed combustion strongly contributes to autoignition of non-premixed mixtures in the particular form of triple flamelets.