Hydrothermal flames occur in aqueous environments at conditions above the critical point of water. Due to the lack of reliable diagnostics applicable to high-pressure, high density-gradient and corrosive environments in hydrothermal flames, the auto-ignition characteristics of hydrothermal flames are still unclear. The objective of this study is to provide a fundamental understanding of auto-ignition process in non-premixed hydrothermal flames in terms of homogeneous ignition calculations and a two-dimensional (2D) direct numerical simulation. To model the real-fluid effects, the Peng-Robinson cubic equation of state with consistent formulas for thermodynamic properties and Chung's high-pressure methods for transport properties are implemented. The homogeneous ignition results indicate that the correlation of the ignition delay time with the mixture fraction in the current study is quite different from those reported in canonical conditions and there is no well-defined "most reactive" mixture fraction. In the DNS, a hydrothermal flame in a 2D mixing layer with pseudo-turbulence is simulated. Auto-ignition occurs independently and ignition kernels form at locations where the local mixture fraction varies from 0.80 to 0.85, lower than the stoichiometric mixture fraction (0.911). The ignition kernels evolve to edge flames that propagate at a mean displacement speed of 1.286 m/s. A compact structure of edge flames is observed, which lacks a rich premixed branch in contrast with the classic triple flame structure. An analysis in terms of species profiles and flame index is carried out to reveal the dynamics of the edge flames. (C) 2018 The Combustion Institute. Published by Elsevier Inc. All rights reserved.