We present a detailed quantum oscillatory study on the Dirac type-II semimetallic candidates PdTe2 and PtTe2 via the temperature and the angular dependence of the de Haas-van Alphen and Shubnikov-de Haas effects. In high-quality single crystals of both compounds, i.e., displaying carrier mobilities between 103 and 104cm2 /Vs, we observed a large nonsaturating magnetoresistivity which in PtTe2 at a temperature T =1.3 K leads to an increase in the resistivity up to (5 ×104 )% under a magnetic field μ0H =62 T. These high mobilities correlate with their light effective masses in the range of 0.04 to 1 bare electron mass according to our measurements. For PdTe2 the experimentally determined Fermi surface cross-sectional areas show excellent agreement with those resulting from band structure calculations. Surprisingly, this is not the case for PtTe2, whose agreement between calculations and experiments is relatively poor even when electronic correlations are included in the calculations. Therefore, our study provides strong support for the existence of a Dirac type-II node in PdTe2 and probably also for PtTe2. Band structure calculations indicate that the topologically nontrivial bands of PtTe2 do not cross the Fermi level ɛF. In contrast, for PdTe2 the Dirac type-II cone does intersect ɛF, although our calculations also indicate that the associated cyclotron orbit on the Fermi surface is located in a distinct kz plane with respect to that of the Dirac type-II node. Therefore, it should yield a trivial Berry phase.