Proportional electroluminescence (EL) in noble gases is used in two-phase detectors for dark matter search to record ionization signals in the gas phase induced by particle scattering in the liquid phase (S2 signals). In this work, the EL pulse-shapes in a two-phase argon detector have for the first time been studied systematically in a wide range of reduced electric field, varying from 3 to 9 Td. The pulse-shapes were studied at different readout configurations and spectral ranges: using cryogenic PMTs and SiPMs, with and without a wavelength shifter (WLS), in the VUV and visible range. We observed the fast component and two unusual slow components, with time constants of about 5 μs and 40 μs. The unusual characteristic property of slow components was that their contribution and time constants increased with electric field.