Antiferromagnetic resonance and two-magnon absorption in an XXZ-chain antiferromagnet <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Cs</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi>CoCl</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:mrow> </mml:math>

Magnetic excitations of the exchange-dipole quasi-one-dimensional XXZ antiferromagnet are studied in the ordered phase. We observe a transformation of the electron spin resonance (ESR) spectrum when crossing the N\'eel temperature near 0.2 K. The single-mode ESR of a correlated XXZ chain transforms in the multimode spectrum in the ordered phase. The multimode spectrum consists mainly of the intensive mode of a single correlated chain, which is surrounded and/or indented by numerous weak satellites. The number of securely fixed modes is eight at $\mathbf{H}\ensuremath{\parallel}b$ and twelve at $\mathbf{H}\ensuremath{\parallel}a$. In addition to the multimode resonance observed at the transverse polarization of the microwave and static magnetic fields, we reveal a wide band of absorption by ($k$,--$k$) pairs of quasiparticles at the longitudinal polarization. This kind of absorption of microwaves occurs both in the ordered and specific spin-liquid phases, revealing the presence of quasiparticles in the specific spin-liquid phase.