When two fires approach each other, convective and radiative heat transfer processes are greatly enhanced. The interaction between two linear fire fronts making an angle θoi between them is of particular interest as it produces a very rapid advance of their intersection point with intense radiation and convection activity in the space between the fire lines. This fire is designated here as a 'jump fire' for when the value of θoi is small, the intersection point of the fire lines can reach unusually high rate of spread values that decrease afterwards in the course of time. A very simple analytical model based on the concept of energy concentration between the fire lines is proposed to explain this behaviour, which in large-scale fires can be of great concern to personnel and property safety. Experimental tests performed at laboratory scale on a horizontal fuel bed confirmed the basic assumptions of the model and provide a framework to extend the present analysis to more general conditions, namely to explain the behaviour of real fires. Given the rapid changes in fire behaviour, 'jump fires' can be considered as a form of extreme fire behaviour.