Honeycomb bodies, especially those used in an exhaust system of an internal combustion engine, contain a housing and a metal matrix with an average starting diameter. The matrix is connected to the housing, whereby at least one contraction limiter that causes an outward directed tensile stress in at least one part of the matrix is provided. The average starting diameter of the matrix is reduced by 5%, preferably by a maximum of 2%, during and/or after being subjected to thermal stress.