Method of relighting several flamed-out engines in a set of N engines of an aircraft in flight, N ≥ 2, the method being implemented by an automated in-flight engine relighting management system that includes controllers , each engine of the aircraft being managed by one of said controllers , wherein each controller , which is in charge of one of said engines i of said set, i = 1,...,N, and which detects that said engine i has flamed out, executes the following steps: - cutting off the energy supply to said engine i ; - windmilling said engine i ; - checking whether at least one other engine of said set has flamed out; - if no other engine of said set has flamed out, attempting to relight said engine i ; characterized in that , if at least one other engine j, j = 1,...,N, j ≠ i, of said set has flamed out, at least one of said controllers effects an engine relighting prioritization including the following steps: - collecting , from the controllers in charge of said engines , information concerning the state of health of each engine ; - determining , from the collected information, information representing a probability of relighting each flamed-out engine; - determining a sequential order of relighting the flamed-out engines as a function of the information representing the probability of relighting each flamed-out engine; and - keeping the engine i windmilling, using the controller in charge of said engine i, until said engine i is selected in the sequential order of relighting the flamed-out engines. wherein each controller , which is in charge of one of said engines i of said set, i = 1,...,N, and which detects that said engine i has flamed out, executes the following steps: - cutting off the energy supply to said engine i ; - windmilling said engine i ; - checking whether at least one other engine of said set has flamed out; - if no other engine of said set has flamed out, attempting to relight said engine i ; - cutting off the energy supply to said engine i ; - windmilling said engine i ; - checking whether at least one other engine of said set has flamed out; - if no other engine of said set has flamed out, attempting to relight said engine i ; characterized in that , if at least one other engine j, j = 1,...,N, j ≠ i, of said set has flamed out, at least one of said controllers effects an engine relighting prioritization including the following steps: - collecting , from the controllers in charge of said engines , information concerning the state of health of each engine ; - determining , from the collected information, information representing a probability of relighting each flamed-out engine; - determining a sequential order of relighting the flamed-out engines as a function of the information representing the probability of relighting each flamed-out engine; and - keeping the engine i windmilling, using the controller in charge of said engine i, until said engine i is selected in the sequential order of relighting the flamed-out engines. - collecting , from the controllers in charge of said engines , information concerning the state of health of each engine ; - determining , from the collected information, information representing a probability of relighting each flamed-out engine; - determining a sequential order of relighting the flamed-out engines as a function of the information representing the probability of relighting each flamed-out engine; and - keeping the engine i windmilling, using the controller in charge of said engine i, until said engine i is selected in the sequential order of relighting the flamed-out engines. <EOS>