  We explore numerically, analytically, and experimentally the relationship
between quasi-normal modes (QNMs) and transmission resonance (TR) peaks in the
transmission spectrum of one-dimensional (1D) and quasi-1D open disordered
systems. It is shown that for weak disorder there exist two types of the
eigenstates: ordinary QNMs which are associated with a TR, and hidden QNMs
which do not exhibit peaks in transmission or within the sample. The
distinctive feature of the hidden modes is that unlike ordinary ones, their
lifetimes remain constant in a wide range of the strength of disorder. In this
range, the averaged ratio of the number of transmission peaks $N_{\rm res}$ to
the number of QNMs $N_{\rm mod}$, $N_{\rm res}/N_{\rm mod}$, is insensitive to
the type and degree of disorder and is close to the value $\sqrt{2/5}$, which
we derive analytically in the weak-scattering approximation. The physical
nature of the hidden modes is illustrated in simple examples with a few
scatterers. The analogy between ordinary and hidden QNMs and the segregation of
superradiant states and trapped modes is discussed. When the coupling to the
environment is tuned by an external edge reflectors, the superradiace
transition is reproduced. Hidden modes have been also found in microwave
measurements in quasi-1D open disordered samples. The microwave measurements
and modal analysis of transmission in the crossover to localization in quasi-1D
systems give a ratio of $N_{\rm res}/N_{\rm mod}$ close to $\sqrt{2/5}$. In
diffusive quasi-1D samples, however, $N_{\rm res}/N_{\rm mod}$ falls as the
effective number of transmission eigenchannels $M$ increases. Once $N_{\rm
mod}$ is divided by $M$, however, the ratio $N_{\rm res}/N_{\rm mod}$ is close
to the ratio found in 1D.
