Abstract: The present invention relates to a method of dyeing a substrate comprising (i) elastomeric fibre containing at least 30 wt. % of a first polymer having a glass transition temperature T of less than 60° C. and (ii) non-elastomeric companion fibre containing more than 50 wt. % of a second polymer, said second polymer being polymer having no glass transition temperature or polymer Shaving a glass transition temperature T2 that is at least 20° C. higher than T1, said method comprising: a) contacting the substrate with a dyeing medium to produce a pre-dyed substrate comprising 10 dyed elastomeric fibre and dyed companion fibre; b) contacting the pre-dyed substrate with an extraction medium at a temperature Te and a pressure Pe, to produce a high fastness dyed substrate, said extraction medium comprising at least 50 wt. % of supercritical or liquefied carbon dioxide; wherein Te exceeds Tg1,extraction and wherein Te is less than Tg2,extraction in case the companion 1 fibre contains more than 50 wt.