An analysis of emulsion data on the K- meson capture reaction on oxygen, K-16O --> pi(-) p(Lambda)(15)N reveals the formation of two intermediate states of the hypernucleus O-16(Lambda)* which subsequently decay by proton emission. The states are relatively broad, as expected for e-values of a few MeV, and are attributed to the 0(+) and 2(+) levels of O-16(Lambda) from the configurations [(P-1/2)(N)(-1) (P-1/2,P-3/2)(Lambda)] with it-binding energies equal to 1.54 +/- 0.09 MeV and 3.10 +/- 0.08 MeV, respectively, where B-Lambda for 15(Lambda)N is 13.59 MeV. The 2(+)-0(+) B-Lambda difference is almost independent of the present statistical error (+/-0.15 MeV) on B-Lambda(N-15(Lambda)). Provided the state more abundantly produced is assigned to the 2(+) level, their relative positions and production rates agree well with the theoretical predictions, A comparison with results from counter experiments is made. The extraction of the it spin-orbit splitting from the 2(+)-0(+) energy difference is discussed using calculations for several different Lambda N potentials. (C) 1997 Elsevier Science B.V.