Anisotropic materials with different signs of components of the permittivity tensor are called indefinite materials. Known realizations of indefinite media suffer of high absorption losses. We show that periodic arrays of parallel carbon nanotubes (CNTs) can behave as a low-loss indefinite medium in the infrared range. We show that a finite-thickness slab of CNTs supports the propagation of backward waves with small attenuation in an ultra-broad frequency band. In prospective, CNT arrays can be used for subwavelength focusing and detection, enhancing the radiation efficiency of small sources. PACS numbers: 78.67.Pt, 61.48.De, 77.84.Lf, 41.20.Jb Metal-dielectric nanostructures [1,2] have already brought applications to microscopy and sensing [3] and have the potential for realization of future nanosized optical devices and circuits [4]. In 2003 the authors of [5] noticed the potential of so-called indefinite metamaterials for subwavelength imaging of objects at electrically large distances from them (the concept of such imaging was first introduced in [6]). Indefinite metamaterials are artificial uniaxial materials in which the axial and tangential components of the permittivity and permeability tensors have different signs. In these materials the isofrequency surfaces have hyperbolic shape. This results in a possibility to design a "hyperlens", where evanescent near fields are transformed into propagating modes and can be transported at electrically long distances [7].The main challenge on the way to realize this and other effects is in the realization of low-loss indefinite materials. For waves of only one linear polarization (TM-polarized waves with respect to the axis of positive permittivity) it is enough to realize a layer of an indefinite dielectric metamaterial [8], whose permeability is unity and only components of the permittivity tensor have different signs. For the visible range such a metamaterial was designed in [8] as an array of parallel plasmonic (metal) nanowires. Since all plasmonic phenomena are related to strong dissipation, the axial component of the permittivity has a significant imaginary part which strongly restricts the subwavelength imaging property of the hyperlens [8]. In the microwave range, materials with negative permittivity can be realized as arrays of thin metal wires [9,10]. However, if the field varies along the wires, the properties of the structure are more complicated that those of a continuous medium due to strong spatial dispersion [11]. The spatial dispersion can be suppressed partially [12] or even totally [13][14][15]. However, manufacturing of structures [12-15] becomes a challenge already at millimeter waves as dimensions need to be quite small for high-frequency applications. For electromagnetic waves in the THz and mid infrared (MIR) range there are no known structures with an indefinite permittivity tensor. The imaginary and real parts of complex permittivity of metals in this range are of the same order and rather high.Here we show that arrays of metallic carb...