We study features of the resonances X(2100) and X(2239) by treating them as the axial-vector and vector tetraquarks with the quark content ss (ss) over bar, respectively. The spectroscopic parameters of these exotic mesons are calculated in the framework of the QCD two-point sum rule method. Obtained prediction for the mass m = (2067 +/- 84) MeV of the axial-vector state is in excellent agreement with the mass of the structure X (2100) recently observed by the BESIII Collaboration in the decay J/psi -> phi eta eta' as the resonance in the f phi eta' mass spectrum. We also explore the decays X(2100) -> phi eta' and X(2100) -> phi eta using QCD light-cone sum rule approach and technical methods of the soft-meson approximation. The width of the axial-vector tetraquark, Gamma =(130.2 +/- 30.1) MeV, saturated by these two processes is comparable with the measured full width of the resonance X(2100). Our prediction for the vector ss (ss) over bar tetraquark's mass (m) over tilde = (2283 +/- 114) MeVis consistent with the experimental result (2239.2 +/- 7.1 +/- 11.3) MeVof the BESIII Collaboration for the mass of the resonance X(2239). (C) 2019 The Author(s). Published by Elsevier B.V.