Features of the fire-protection modification by phosphorus-containing fire retardants of textiles made of various chemical and natural fibres through the action of multi-photon continuous CO 2 -laser radiation were examined. A mathematical description was obtained. The optimum modification parameters were determined. The advantages of the developed technology over the traditional one were demonstrated.Fire protection of household and technical cloths, woven and non-cloth materials, is important because textiles exhibit elevated combustibility and are often the source and propagator of fires. Many countries have adopted regulations prohibiting the use of combustible textiles for preparing items designated for household (clothes, table and personal linens, curtains, tablecloths, etc.) and technical (tents, pavilions, building trim, furniture upholstery, vehicle interiors, etc.) use. However, the use of fire-protected materials in Russia is still limited, primarily for the preparation of protective clothing, because of the high cost of manufacturing thermally resistant synthetic materials and also the lack of effective ecologically safe fire retardants (FRs) and innovative fire-protection technologies for multi-ton chemical and natural textile fibres and cloths. Therefore, the development of effective fire-protection technologies is a critical problem.The fire-protection process parameters must be determined in order to modify textile fibres and cloths through the action of continuous multi-photon CO 2 -laser radiation (LR). The LR energy needed to produce a given structure that provides high operational properties to the fibres was calculated quantitatively taking into account the energy features of the initial structure of the material to be irradiated and its thermal stability. The main goal of the calculations was to determine the LR power density (W p ) delivered per unit area of treated textile surface and the duration of the LR action. The calculations were made starting with the conditions for rupture of selected types of chemical bonds (···C-O-, ···C=O, ···C-H) that had the same frequency (900-1100 cm -1 ) as the CO 2 -laser radiation and were present in the fibre-forming polymer macromolecules and the FRs [3][4][5].The energy characteristic for bond stability is the bond energy (E b ). The greater E b is, the more energy must be spent to rupture the bond. Each bond should fulfill the following condition in order to achieve dissociation (rupture):where ΣE b is the sum of bond dissociation energies in the volume of material to be irradiated; E 1 , the dissociation energy of one bond; and E tot , the total delivered LR energy. Let the intensity of incident light E tot at the entrance to material of area 1 m 2 and thickness h decrease as it penetrates through the porous textile structure by E h according to the Bouguer-Lambert lawwhere g is the natural absorption index of LR by the sample.

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