The reduction of maintenance and replacement work costs is an important driving force in the development of high temperature materials (T>800 °C) that can autonomously heal damage as a result of local cracks. In recent years some potential routes involving the addition of sacrificial particles have been identified, yet these systems have the drawback of reduced initial properties and being capable of healing cracks only once. Hence there is a need for high temperature materials with high initial properties and an ability to heal cracks several times. Ti2AlC, being a member of the MAX-Phase ceramics family has shown an unusual ability to heal cracks multiple times through selective oxidation of Al, while maintaining its salient mechanical properties [1]. It is to be expected that other compounds of the Mn+1AXn family, where M is a transition metal, A an element from groups 13 or 14 and X either Carbon or Nitrogen combining characteristics of metals and ceramics, may also show self-healing abilities. In this work MAX phases known to date (approx. 85) have been evaluated to establish a group of potential compounds expected to be promising applicants of (multiple) crack-healing. To this end, their thermodynamics and material transport at elevated temperatures determining the selective oxidation kinetics and crack filling potential have been considered. MAX phases with Al and Si are of special interest since the oxides of these A elements have been shown to act successfully as healing agents [2, 3]. While not having been explored, MAX phases which in combination with the oxidation of the M element form a single ternary oxide may also offer attractive self-healing potential. MAX phases that show an above average potential for self-healing have been identified, in order to guide the experimental research into the wider exploration of MAX phase ceramics for intrinsic high temperature self-healing ceramics.