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Photothermal effects are studied under laser irradiation of aqueous suspensions of gold nanorods (in vitro experiments) and mice-inoculated Erlich carcinoma after intravenous injection of gold nanorods with the size 40 Multiplication-Sign 10 nm and plasmon resonance at the wavelength 810 nm (in vivo experiment). In 24 hours after the injection the polyethylene-glycol-coated nanoparticles accumulated in the tumour with the concentration three - four times greater than in healthy muscle tissue. At concentrations, attained as a result of passive accumulation of nanoparticles in the tumour (4 {mu}g per 1 g of tumour), the efficiency of the tumour heating was higher than that in aqueous solutions having the same concentration of nanoparticles. Various mechanisms of this effect are discussed including the difference in thermal physical parameters of water and biotissue, the aggregation of nanoparticles in tissues, the influence of multiple scattering in biotissue, and the nonuniform accumulation of particles in the tumour. Using the Monte Carlo method for simulating multiple scattering of light, it is shown that there are such proportions between the biotissue scattering coefficient and the absorption coefficient of nanoparticles, at which the fraction of absorbed photons in the tissue is higher than that in a transparent medium containing the same nanoparticles. The conclusion is made that the regime of hyperthermia is less efficient for antineoplastic therapy than the thermal damage due to fast short-time heating of the tissues up to the destruction temperature.