  A search for double beta processes in 190Pt and 198Pt was realized with the
help of ultra-low background HP Ge 468 cm^3 gamma spectrometer in the
underground Gran Sasso National Laboratories of the INFN (Italy). After 1815 h
of data taking with 42.5 g platinum sample, T_{1/2} limits on 2beta processes
in 190Pt (\epsilon\beta^+ and 2\epsilon) have been established on the level of
10^{14}-10^{16} yr, 3 to 4 orders of magnitude higher than those known
previously. In particular, a possible resonant double electron capture in 190Pt
was restricted on the level of 2.9 \times 10^{16} yr at 90% C.L. In addition,
T_{1/2} limit on 2 beta^- decay of 198Pt (2\nu+0\nu) to the 2^+_1 excited level
of 198Hg has been set at the first time: T_{1/2}>3.5 \times 10^{18} yr. The
radiopurity level of the used platinum sample is reported.
