The　hot　deformation　behaviors　of　single-　and　two-phase　CuAlMn　shape　memory　alloy　were　studied.　Isothermal　compression　tests　were　conducted　at　different　temperatures　from　400　degrees　C　to　800　degrees　C　and　various　strain　rates　from　0.001/S　to　1/S.　At　the　temperature　below　500　degrees　C,　CuAlMn　alloy　had　a　two-phase　microstructure　(FCC　alpha　phase　+　L2(1)　beta　phase);　while　at　the　temperature　higher　than　550　degrees　C,　the　alloy　had　a　single　beta　phase　structure.　The　flow　stress　curves　showed　the　stress　drop　for　all　samples,　indicating　a　dynamic　recrystallization　(DRX)　feature　of　the　alloy.　The　local　minimum　value　of　stress　drop　appeared　at　500　degrees　C.　The　thermal　active　energy　(Q)　were　calculated　to　be　418.7　kJ　mol(-1)　for　alpha　+　beta　alloy　at　400-500　degrees　C　and　219.7　kJ　mol(-1)　for　beta　alloy　at　550-800　degrees　C,　respectively.　The　artificial　neural　network　(ANN)　model　showed　a　high　precision　to　predict　the　flow　stress　of　the　studied　alloy　at　a　wide　range　of　temperature.　Based　on　the　dynamic　material　model　(DMM)　theory,　the　processing　map　of　the　alloy　that　consists　of　the　contour　lines　of　the　power　dissipation　factor,　it,　and　the　instability　criteria　was　established.　The　grains　were　refined　to　a　micron　level　and　DRX　of　alpha　phase　occurred　during　the　deformation　between　400　-　500　degrees　C　at　the　low　strain　rate.　The　hot　deformation　behaviors　of　the　alloy　at　the　low　temperature　(400　-　450　degrees　C)　mainly　depended　on　the　deformation　of　alpha　phase.　The　optimum　deformation　parameters　for　the　single-phase　CuAlMn　alloys　were　750-800　degrees　C/0.1-1　s(-1)　.　(C)　2020　Elsevier　B.V.　All　rights　reserved.