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Most of the studies oriented on improving the physical-mechanical properties of the cured epoxy resins by introducing carbon nanotubes (CNTs) are concentrated on the verification of the effect of small concentrations of filler (0.1 to a few percent). However the mass production of epoxy resins modified by CNTs is impossible due to the fact that modern technology development does not allow obtaining sufficient amount of nanotubes. Moreover, the cost of CNTs is several orders higher than cost of epoxy resins, so their use (even at a concentration of ~ 1 wt.%) sharply increases the cost of the products. As a result, it is important to investigate the influence of ultra-low concentrations of nanotubes (0.001 – 0.1 wt. %) on physical-mechanical properties of cured epoxy resins. The influence of ultra-low concentrations (0.001 – 0.1 wt. %) of carboxylated single-wall carbon nanotubes (cSWCNT) on physical-mechanical properties of epoxy-diane resins (epoxide equivalent 182 g/eq) cured by 4,4′-diamino-diphenylmethan was investigated in this work. We used cSWCNT synthesized by arc discharge, and two epoxy resin/curing agent ratios. The first ratio provides the maximum strength of composition, and the second ratio provides the maximum glass transition temperature. It was shown, that increasing of cSWCNT concentration from 0.001 to a 0.1 wt. % leads to 2-4 % increase in the maximum strength of the samples but reduce reproducibility of the measurements. We have supposed that cSWCNT can form agglomerates in epoxy matrix which act as stress concentrators under tensile test, that adversely affects the reproducibility of the measurements. Change in Young's modulus with concentration of cSWCNT have nonmonotonic behaviour. A slight decrease of the Young's modulus values compared with the comparative sample occurs at addition of 0.001 – 0.008 wt. % of cSWCNT. The Young's modulus increases with further increasing of the cSWCNT concentration and at 0.1 wt.% of cSWCNT it became 6-8 % higher than the Young's modulus of the comparative sample. The work was supported by Russian Foundation for Basic Research (grant 13-03-12164 ofr-m).