We have studied the Cretaceous and Paleogene flysch of the Duklya-Chornohora, Burkut, Rakhiv, Marmarosh and Pieniny covers that in the south-eastern sector of the Ukrainian Carpathians near the Romanian border (Hutsulian segment) distinguish themselves by very inclined overthrust. Spatially the given tectonic units are in so-called hydrothermal fluid, unfavourable on the whole as to the presence of hydrocarbons in it on a large scale. But, within its limits the plots, small in area, with hydrocarbon prevalence in the gas composition are distinguished. Prospects for gas presence in the region should be connected with those of them that spatially are drown to the Transcarpathian trough. One such section is the Velikobychkovk sector of the Monastyretsky sub-cover, where it is proposed to lay a parametric well 1-Velikiy Bychkov, in order to reveal the possible para-autochthon of the Vezhany sub-cover and the Paleogene of the Dilovetsky sub-cover. In addition, according to seismic data, a significant rise in the pre-flysch base is forecast in this section of the Carpathians under the Marmarosh cover. The roof of this foundation at the location of the recommended well 1-Velikiy Bychkov may be at a depth of 5000–5500 m. It may be represented by the youngest deposits of the pre-Alpine complex – the Triassic strata, industrially oil and gas saturated in the neighboring countries.