Abstract: Disclosed is a process for the degradation of highly toxic halogenated organic compounds, in particular polychlorinated dibenzodioxins (PCDD) and dibenzofurans (PCDF), contained in gases containing no SO.sub.2 by oxidation using preferably hydrogen peroxide. The SO.sub.2 -free gas is passed, in the presence of hydrogen peroxide, over a substantially inorganic solid contact catalyst, in particular pyrogenic or precipitated silica or aluminum silicate. A residual PCDD/PCDF content of below 0.1 ng TE/Nm.sup.3 may be achieved in the thus treated gas; the highly toxic compounds are oxidized on the solid contact catalyst.