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 (130, 160), 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 (160, 130) 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 (160, 130) 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.