The investigation of the temperature dependences of microwave surface impedance and complex conductivity of V 3 Si single crystals with different stoichiometry allowed to observe a number of peculiarities which are in remarkable contradiction with single-gap Bardeen-Cooper-Schrieffer theory. At the same time, they can be well described by two-band model of superconductivity, thus strongly evidencing the existence of two distinct energy gaps with zero-temperature valuesPACS numbers: 74.25.Nf, 74.70.Ad, 74.20.Fg 1 The story of multi-gap superconductors goes to the middle of the last century, when the extension of Bardeen-Cooper-Schrieffer (BCS) theory [1] was proposed [2, 3]. The followed experimental investigations, however, contradicted each other showing the existence of single gap, multiple gaps and slightly anisotropic gap in various superconducting materials. The interest to this phenomenon has been stimulated by the discovery of two-gap superconductivity in MgB 2 . The existence of at least two different energy bands crossing the Fermi-level (particular feature of MgB 2 ) appears to be the prerequisite for the observation of multiple gaps. The second requirement, as follows from [3], is a weak interband scattering. Such processes can be significantly reduced if wave functions of electrons from two bands have different symmetry. For example this may happen when energy band structure has both flat and non-flat areas near the Fermi level. Flat areas lead to a singularity in the density of states at the Fermi level and can be experimentally detected for instance by non-linear temperature dependence of the resistivity ρ(T ) in the normal state. In the opposite case of more or less similar bands structures even small amount of impurities leads to high interband scattering and almost excludes the possibility to detect multi-gap response of the material. Apparently, the above requirements apply to the layered superconductor NbSe 2 and to A15 structure superconductors Nb 3 Sn, V 3 Si, V 3 Ga, in which the density of states has very high and narrow peak just in the vicinity of the Fermi level according to band-structure calculations [4]. Recently the existence of multiple gaps in Nb 3 Sn polycrystalline sample has been proposed to explain specific heat measurements [5]. The authors of [6] showed the similarity of the magnetic field dependence of thermal conductivity in NbSe 2 to that of MgB 2 and concluded about the presence of the second energy gap in NbSe 2 . Such a similarity was not found in V 3 Si. However, back in 1969 J.Brock denoted the existence of the second gap as one of the possible explanations of the peculiarities seen in the specific heat of V 3 Si [7].The measurements of the temperature dependences of microwave conductivity both in low-T c and high-T c superconductors were very informative. They proved the applicability of BCS theory to conventional superconductors, allowed to distinguish superconductors with different order parameter symmetry and to measure the values of energy gap, penetration depth,...

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Measurements of the microwave surface impedance Zs(T ) = Rs(T ) + iXs(T ) and of the complex conductivity σs(T ) of high-quality, high-Tc single crystals of YBCO, BSCCO, TBCCO, and TBCO are analyzed. Experimental data of Zs(T ) and σs(T ) are compared with calculations based on a modified two-fluid model which includes temperature-dependent quasiparticle scattering and a unique temperature variation of the density of superconducting carriers. We elucidate agreement as well as disagreement of our analysis with the salient features of the experimental data. Existing microscopic models are reviewed which are based on unconventional symmetry types of the order parameter and on novel mechanisms of quasiparticle relaxation.