Some general properties of exciton spectra of an interacting two-dimensional electron-hole system have been established. In the quantum limit both the frequencies and the matrix elements of exciton transitions are independent of environment, i.e., of filling factors of electrons and holes, if all the electron-hole interactions are equal in magnitude, ${\mathit{V}}_{\mathit{e}\mathit{e}}$=${\mathit{V}}_{\mathit{h}\mathit{h}}$=\ensuremath{\Vert}${\mathit{V}}_{\mathrm{eh}}$\ensuremath{\Vert}. Only when these symmetry restrictions are lifted, do the absorption and emission spectra acquire nontrivial properties reflecting electronic correlations in a system. We consider an exciton against the background of an incompressible quantum liquid for both symmetric and nonsymmetric systems. It is always strongly coupled to the environment. This interaction may be considered as a polaron effect that is due to the dressing of an exciton by magnetorotons, but it shows very specific features because of restrictions imposed by the Pauli exclusion principle. The energy spectrum of a dressed exciton, the electric charge distribution, and some other properties of it are investigated. When the anisotropy parameter reaches its critical value the absolute minimum of the energy spectrum shifts from the point k=0 to a circle, as a result of which abrupt changes in the emission spectrum are expected. A model of the ground state is proposed.