TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Process: In the process, the fatty acids are obtained by physical refining including: a steam distillation; vacuum distillation of fats and oils; hydrolysis of triglycerides of fats and oils; or by acidulation of soaps. In the process: the refined oils are fractioned into phases-L and S by a fractional crystallization method comprising controlled cooling down during which the triglycerides of the complex mixture with substantially saturated acyl-moieties crystallize and precipitate from the mixture forming the phase-S, while the triglycerides with substantially unsaturated acyl-moieties remain as liquids forming the phase-L, and both the phases are then separated by simple filtration, decantation or centrifugation; and the phase-L is trans-esterified with 1-5C mono-functional alcohol in order to produce alkyl fatty esters as bio-diesel and glycerol; the fatty acid soaps are obtained by saponification of fats and oils, by chemical refining including neutralization of free fatty acids present in the fats and oils, or by neutralization of fatty acids obtained from hydrolysis of the fats and oils; and the phase-S is transformed into linear or substantially linear paraffins as bio-naphtha together with bio-propane by hydro-deoxygenation in the presence of hydrogen and at least one catalyst including nickel, molybdenum, cobalt, nickel-tungsten, nickel-molybdenum, cobalt-molybdenum, nickel-cobalt-tungsten, nickel-cobalt-molybdenum, nickel-molybdenum-tungsten, cobalt-molybdenum-tungsten oxides or sulfides as catalytic phase, preferably supported on high surface area carbon, alumina, silica, titania or zirconia. The phase-S is transformed into linear or substantially linear paraffins as bio-naphtha by hydrolysis into glycerol and fatty acids, removal of the glycerol, or by physical refining including steam distillation or vacuum distillation of fats and oils, or obtained by acidulation of soaps and hydro-deoxygenation or decarboxylation of the fatty acids, where: the hydro-deoxygenation or decarboxylation is conducted in the presence of hydrogen and the catalyst as catalytic phase, preferably supported on high surface area carbon, alumina, silica, titania or zirconia or group-10 (nickel, platinum and palladium) and group-11 (copper and silver) metals or alloy mixtures supported on high surface area carbon, magnesia, zinc oxide, spinels (magnesium-aluminum oxide and zinc-aluminum oxide) ,the perovskites, calcium silicates (like xonotlite), alumina, silica and/or silica-alumina's; and the decarboxylation of the fatty acids is carried out on basic oxides, like alkaline oxides, alkaline earth oxides, lanthanide oxides, zincoxide, the spinels, perovskites, calcium silicates (like xonotlite) , either as bulk material or dispersed on neutral or basic carriers, on basic zeolites (like alkali or alkaline earth low silica/alumina zeolites obtained by exchange or impregnation). The hydrodeoxygenation is carried out at 200-500 degrees C, under a pressure of 1-10 MPa (10-100 bars) and with a hydrogen to feed ratio of 100-2000 Nl/l, and the decarboxylation is carried out at 100-550 degrees C, under a pressure of 0.1-10 MPa (1 to 100 bars) and with a hydrogen to feedstock ratio from 0 to 2000 Nl/l. The decarboxylation of the soaps is carried out at 100-550 degrees C under pressure of 0.1-10 Mpa, in presence of water, and with a water to feedstock ratio of at least 1 mole water per mole of soap. The feedstock is mixed with steam in a ratio of 0.2-1 kg, preferably 0.3-0.5 kg steam per kg feedstock, and the mixture is heated up to 750-950 degrees C at a residence time of 0.05-0.5 seconds. Preferred Components: The complex mixture of naturally occurring fats and oils includes vegetable oils and animal fats, preferably inedible oils, highly saturated oils, waste food oils and/or by-products of the refining of vegetable oils. EXAMPLE - No suitable example given.