A porous body which has a density of from 40 to 70%, is formed from an Fe-based alloy and contains from 0.01 to 2% by weight of mixed oxide with at least one oxidic compound of one or more metals from the group consisting of Y, Sc, rare earth metals and at least one further oxidic compound of one or more metals from the group consisting of Ti, Al, Cr. The porous body displays no after-shrinkage even at operating temperatures of 900° C., it has very good corrosion resistance and it is particularly suitable as a support substrate for use in high-temperature fuel cells.