RDX containing a small amount of single-walled carbon nanotubes is obtained by the method of co-precipitation out of a solution. The detonation of this composition is studied by an electromagnetic method of mass velocity measurement and by a high-resolution electroconductivity method. A clearly expressed chemical spike is observed. Preliminary indications of reaction acceleration in the presence of nanotubes are obtained. The electroconductivity measurements are complicated because of the noticeable conductivity of the original material; if this factor is taken into account, the electrical conductivity profiles behind the detonation front are similar to those observed for pure RDX. Possible reasons for the influence of nanotubes on detonation characteristics are discussed.