A new procedure to quantify the components of oceanic helium (terrigenic 3He and 4He released from the ocean floor and tritiugenic 3He from tritium decay) is described. Terrigenic He and nonatmospheric 3He (i.e., terrigenic and tritiugenic combined) are obtained in terms of measured concentrations of the He isotopes and also of neon (Ne) (which improves the separation considerably), assuming terrigenic He to vanish in the mixed layer. For the subsequent separation of terrigenic and tritiugenic 3He, additional information is required and 3He due to natural tritium represents a complication. The procedure is applied to data from a hydrographic section in the South Atlantic (19 ¿S, 1991) and one in the Eastern Mediterranean (1987). The 1&sgr; data precisions and a systematic error accounting for uncertainties in mixed-layer He are approximately 0.3%. Sections of the new representations of oceanic He and 3He and comparisons to the nearest classical quantities (i.e., 3He, He) are presented. In the South Atlantic the 3He distribution reflects the hydrographic structure. East of 20 ¿W the average 3He/4He ratio of terrigenic He below 800 m is 4.5¿0.8 times the atmospheric ratio, which implies a substantial contribution of crustal He. In the upper waters, tritiugenic 3He (0.5 tritium units, ¿20%) is separated from terrigenic 3He. In the Eastern Mediterranean, tritiugenic 3He is quantified throughout the water column in the presence of substantial levels of terrigenic He; the release rate of terrigenic He from the sea floor is found to be 3.1¿1.21010 atoms m-2 s-1, similar to the rate for continental crust, with a mantle He contribution of 5¿1.2% only. Recommendations for future work are to reduce the mentioned systematic error and the uncertainty margins of the He and Ne solubilities and of 3He due to natural tritium. ¿ 1998 American Geophysical Union