A method for producing power using an initial fluid (102, 202, 302, 402, 502) in a condensed state, the method comprising: (a) pumping (104, 204, 304, 404, 504) fluid derived from the initial fluid to form pumped fluid at above the fluid's critical pressure; (b) heating (106/108/112/114/118, 206/208/210, 306/308/310, 406/408/410, 506/508/510/512/514/516/518) fluid derived from the pumped fluid to form superheated supercritical heated fluid; (c) expanding (120, 212, 312, 412, 520) fluid derived from the superheated supercritical heated fluid in at least one first power-producing expansion step to form superheated sub-critical-pressure expanded fluid; and (d) cooling and re-condensing fluid derived from the superheated subcritical-pressure expanded fluid CHARACTERISED IN THAT: the fluid derived from the superheated subcritical-pressure expanded fluid is cooled and re-condensed against the fluid derived from the pumped fluid in a gasifying/condensing heat exchanger (106, 206, 306, 406, 506) to form re-condensed fluid in a liquid state, wherein the re-condensing of the fluid derived from the superheated subcritical-pressure expanded fluid provides heat to gasify the fluid derived from the pumped fluid in the gasifying/condensing heat exchanger; and the method further comprising: (e) pumping (126, 218, 316, 418, 526) fluid derived from the re-condensed fluid to form re-pumped fluid at above the fluid's critical pressure; (f) heating (128/122, 220/214/222, 318/320/322/324, 420/422/414/424, 528/530/532/522/534/536) fluid derived from the re-pumped fluid at above the fluid's critical pressure to form re-heated fluid; and (g) expanding (130, 224/230/234, 326/330, 426/430, 538) fluid derived from the re-heated fluid in at least one second power-producing expansion step to form re-expanded fluid, with (232, 428) or without (228, 328) reheating between expansion steps if step (g) comprises more than one second power-producing expansion step (224/234, 224/230), 326/330, 426/430). (a) pumping (104, 204, 304, 404, 504) fluid derived from the initial fluid to form pumped fluid at above the fluid's critical pressure; (b) heating (106/108/112/114/118, 206/208/210, 306/308/310, 406/408/410, 506/508/510/512/514/516/518) fluid derived from the pumped fluid to form superheated supercritical heated fluid; (c) expanding (120, 212, 312, 412, 520) fluid derived from the superheated supercritical heated fluid in at least one first power-producing expansion step to form superheated sub-critical-pressure expanded fluid; and (d) cooling and re-condensing fluid derived from the superheated subcritical-pressure expanded fluid CHARACTERISED IN THAT: the fluid derived from the superheated subcritical-pressure expanded fluid is cooled and re-condensed against the fluid derived from the pumped fluid in a gasifying/condensing heat exchanger (106, 206, 306, 406, 506) to form re-condensed fluid in a liquid state, wherein the re-condensing of the fluid derived from the superheated subcritical-pressure expanded fluid provides heat to gasify the fluid derived from the pumped fluid in the gasifying/condensing heat exchanger; and the method further comprising: (e) pumping (126, 218, 316, 418, 526) fluid derived from the re-condensed fluid to form re-pumped fluid at above the fluid's critical pressure; (f) heating (128/122, 220/214/222, 318/320/322/324, 420/422/414/424, 528/530/532/522/534/536) fluid derived from the re-pumped fluid at above the fluid's critical pressure to form re-heated fluid; and (g) expanding (130, 224/230/234, 326/330, 426/430, 538) fluid derived from the re-heated fluid in at least one second power-producing expansion step to form re-expanded fluid, with (232, 428) or without (228, 328) reheating between expansion steps if step (g) comprises more than one second power-producing expansion step (224/234, 224/230), 326/330, 426/430). (e) pumping (126, 218, 316, 418, 526) fluid derived from the re-condensed fluid to form re-pumped fluid at above the fluid's critical pressure; (f) heating (128/122, 220/214/222, 318/320/322/324, 420/422/414/424, 528/530/532/522/534/536) fluid derived from the re-pumped fluid at above the fluid's critical pressure to form re-heated fluid; and (g) expanding (130, 224/230/234, 326/330, 426/430, 538) fluid derived from the re-heated fluid in at least one second power-producing expansion step to form re-expanded fluid, with (232, 428) or without (228, 328) reheating between expansion steps if step (g) comprises more than one second power-producing expansion step (224/234, 224/230), 326/330, 426/430).