This dissertation examines stabilisation processes in turbulent non-premixed jet flames, created by injecting gaseous fuel into a co-flowing stream of hot, low-oxygen combustion products. Being able to predict whether and how a flame achieves stable and reliable combustion is a matter of great practical relevance, and a challenging scientific problem. Several theories have been developed to describe the flame stabilisation of conventional non-premixed flames, i.e., flames where cold gaseous fuel is injected in cold air or oxygen. There is however no theory that specifically describes how a non-premixed flame is stabilised when the oxidiser stream is pre-heated, such that autoignition might be a dominant factor in the stabilisation process. A substantial part of this work is devoted to examining how flame stabilisation works under these circumstances and how different parameters impact this process. The experimental studies that form the basis of this work are carried out on the Delft jet-in-hot-coflow (DJHC) burner. The coflow of this burner is operated at a maximum temperature between approximately 1390K to 1540K, and at a typical oxygen mass fraction ranging from 7.6% to 10.9%. This experimental setup was developed with the aim of mimicking some aspects of flameless combustion, a combustion technique that combines high efficiencies with low pollutant emissions. The design of the DJHC burner is based on the Adelaide jet-in-hot-coflow burner, modified to allow for the addition of seeding particles for velocity measurements. The fuels used in the jet are Dutch natural gas and synthetic mixtures that approximate Dutch natural gas.