The　cascade　refrigeration　system　and　cascade　air　source　heat　pump　have　both　been　a　well-known　advanced　technology　for　providing　cooling　and　heating　under　certain　circumstances.　The　intermediate　temperature　has　been　proven　as　a　key　factor　in　affecting　the　operating　performance　for　both　the　refrigeration　and　heat　pump　system.　However,　the　optimal　intermediate　temperature　varies　along　with　the　change　of　the　ambient　temperature,　cooling/heating　demand.　So　achieving　the　real-time　optimal　intermediate　temperature　in　a　realistic　operating　circumstance　is　critical　for　improving　the　performance　of　cascade　refrigeration　or　heat　pump　system.　In　this　paper,　the　extreme　seeking　control　strategy　is　proposed　to　optimize　the　coefficient　of　performance　via　seeking　the　real-time　optimal　intermediate　temperature.　A　cascade　refrigeration　system　model　and　a　cascade　air　source　heat　pump　water　heater　model　are　built　based　on　Modelica,　and　the　ASHP　water　heater　model　is　validated　by　experimental　data.　The　simulations　are　conducted　under　fixed　and　variable　operating　conditions　to　validate　the　effectiveness　of　the　proposed　strategy.　©　2020