A fluid pump (10) or motor (100) includes a pair of enmeshed tapered rotors (22,24,122,124) having intersecting axes of rotation. The first rotor (22,122) includes a small low pressure end (34,54,134,154) and a larger high pressure end (32,52,132,152) and a spiral thread (36,56,136,156) that increases in width and depth as it progresses from the high pressure end (28,128) to the low pressure end (26,126). The second rotor (24,124) enmeshes with the first rotor (22,122), and has an identical structure, except that its threads (36,56,136,156) progress in the opposite direction. Both rotors (22,24,122,124) are mounted on sliding splines (42,62,142,162) which permit them to move, to a limited extent, into and out of their respective receiving cavities. The pressure on the high side (28,128) of the pump (10) or motor (100) tends to urge the rotors (22,122,24,124) against the walls (16,20,116,120) of the receiving cavities thereby improving their sealing capabilities and the overall efficiency of the pump (10) or motor (100) as a whole.