This　study　has　determined　the　optimal　ratios　of　heat　conductance　of　a　cold-side　heat　exchanger　to　that　of　a　hot-side　heat　exchanger　when　the　heating　load　and　the　coefficient　of　performance　(COP)　of　the　irreversible　air　heat　pump　cycles　are　taken　as　the　optimization　objectives.　Both　the　optimum　distributions　of　heat　conductance　corresponding　to　the　maximum　heating　load　and　the　maximum　COP　are　less　than　0.5　for　the　fixed　total　heat　exchanger　inventory.　The　influences　of　the　heat　reservoir　temperature　ratio,　the　total　heat　exchanger　inventory,　and　the　efficiencies　of　the　compressor　and　expander　on　the　optimum　distribution　of　heat　conductance　and　the　maximum　heating　load　and　the　maximum　COP　are　analysed　and　shown　by　numerical　examples.　©　2010　Taylor　and　Francis.