A purified thermostable enzyme is derived from the thermophilic archaebacterium Archaeoglobus fulgidus. The enzyme can be native or recombinant, is stable under PCR conditions and exhibits double strand specific exonuclease activity. It is a 3-5 exonuclease and cleaves to produce 5-mononucleotides. Thermostable exonucleases are useful in many recombinant DNA techniques, in combination with a thermostable DNA polymerase like Tag especially for nucleic acid amplification by the polymerase chain reaction (PCR).