Simultaneous excitation of several valence electrons in atoms gives rise to a dense spectrum of compound autoionizing states (AIS). These states are almost chaotic superpositions of large numbers of many-electron basis states built of single-electron orbitals. The mean level spacing D between such states is very small (e.g., D<0.01 eV for the numerical example of J(pi)=4(-) states of Ce just above the ionization threshold). The autoionization widths of these states estimated by perturbations, gamma=2 pi\W\(2), where W is the Coulomb matrix element coupling the AIS to the continuum, are also small, but comparable with D in magnitude: gamma similar to D. Hence the nonperturbative interaction of AIS with each other via the continuum is very essential. It suppresses greatly the widths of the autoionizing resonances (Gamma similar or equal to D-2/3 gamma much less than D), and leads to the emergence of a ''collective'' doorway state which accumulates a large share of the total width. This state is in essence a modified single-particle continuum decoupled from the resonances due to its large width. Narrow compound AIS should be a common feature of atomic spectra at energies sufficient for excitation of several electrons above the groundstate configuration. The narrow resonances can be observed as peaks in the photoabsorption, or, in electron-ion scattering, as Fano-type profiles on the background provided by the wide doorway-state resonance. It is also shown that the statistics of electromagnetic and autoionization amplitudes involving compound states are close to Gaussian.