This paper reports the results of the first measurements of the thermal conductivity of the a, )3, and y phases of solid oxygen over the temperature range of 1-52 K. A simple qualitative analysis was performed to explain the observed anomalies in thermal conductivity, which manifested themselves by a jump at the a-fi transition, the anomalously weak temperature dependence in the p phase, and an increase of the conductivity with temperature in the y phase.PACS numbers: 66.70.+f, 31.70.Ks, 75.20.Ck, Solid oxygen, a unique crystal combining properties of a molecular crystal and a magnet, has been a subject of intensive experimental and theoretical studies during the last two decades (see, for example [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], and references therein). The following picture has emerged as a result of those studies. Oxygen exists under the equilibrium vapor pressure in three crystalline modifications. The orientationally ordered monoclinic low temperature a phase (C2/m) is a collinear two-sublattice quasi-2D antiferromagnet. The phase transition (7^ = 23.9 K) into the intermediate rhombohedral /3 phase (R3m) is associated with the transformation of the magnetic structure. The nature of this transformation is still a subject for discussion [13].Though none of the measured thermodynamic characteristics as well as the molar volume [5] show any jump at the a-fi transition point and, moreover, the heat of transition has not been detected in precise calorimetric study [3], the a-p transformation is beyond all doubts a first order phase transition. This conclusion follows, for instance, from the observation of hysteresis of the magnetization curves at the transition [11].The long-range magnetic order in /3-oxygen is most probably absent; however the short-range order with the correlation length of 5 A in three-sublattice or incommensurate helicoidal structures persists over the whole range of the existence of the phase [ 11,14,15].Both the low temperature phases have the same orientational structure in which the molecular axes are collinear and perpendicular to the close packed layers. The spectrum of elementary excitations in the a phase consists of (besides acoustic modes) two libron modes at 43 and 78 cm -1 [2] and two magnon ones at 6.4 and 27 cm -1 [1,4]. No magnon excitations were found in the p phase and there is one twofold degenerated libron mode at 50 cm" 1 [2].The p-y transition (7^=43.8 K) is accompanied by a radical rearrangement of the lattice, a considerable jump (5.4%) of volume [5], and high value of the latent heat of the transition [3]. The y phase has an eight-molecule cubic cell with an orientationally disordered structure with Pm3n symmetry. It exhibits paramagnetic properties with a quasi-ID magnetic short-range order [9,10].In this paper we report results of the first measurements of the thermal conductivity of the a, /?, and y phases of solid oxygen.The measurements of the thermal conductivity were carried out by the stationary heat flux method over a temperature ran...