The invention relates to copolymer (PVDF-co-F6PP) or polymer (PVDF) nanofibrous or nanostructured flat membranes for direct contact distillation, which allow a considerable reduction in heat loss due to conduction and the polarisation of temperatures and concentrations since said membranes have high permeate flows and which reduce the energy requirement of the direct contact membrane distillation (DMCD) process. The membranes are produced by means of electrospinning with solvents having different affinities with the polymer or copolymer used, thereby allowing the thickness of the membrane, the diameter of the nanofibres and the pore size of the membranes (empty space between nanofibres) to be controlled. The resulting membranes can be used in DMCD for different purposes, such as salt water treatment, wastewater treatment, concentration of pharmaceutical products and foods or the production of distilled water or ultrapure water.