Two-dimensional double-quantum (2D2Q) 35Cl NMR spectra of systems exhibiting electric quadrupolar effects have been obtained. Single-crystal type spectra (type a) result from magnetic field-oriented lyotropic liquid crystalline samples containing Cl- ions. Inhomogeneous powder patterns (type b) result from unoriented lyotropic liquid crystalline samples. A homogeneous biexponentially relaxed spectrum (type c) results from a sufficiently concentrated solution of a macromolecule in Cl-containing medium. The theory of the 2D2Q experiment on isolated spin-2 systems producing type a spectra has been elaborated. The effects of variation of the flip angle of the read pulse and offset of the excitation frequency have been derived. Experimental manifestations of these effects have been recorded. The recovery of the spectrum of an oriented lyotropic liquid crystalline sample after a sample rotation in the spectrometer magnetic field provides an example of transient, partial NMR invisibility in the one-dimensional single-quantum 35Cl NMR spectrum.