  We study the relation between quasi-normal modes (QNMs) and transmission
resonances (TRs) in one-dimensional (1D) disordered systems. We show for the
first time that while each maximum in the transmission coefficient is always
related to a QNM, the reverse statement is not necessarily correct. There
exists an intermediate state, at which only a part of the QNMs are localized
and these QNMs provide a resonant transmission. The rest of the solutions of
the eigenvalue problem (denoted as strange quasi-modes) are never found in
regular open cavities and resonators, and arise exclusively due to random
scatterings. Although these strange QNMs belong to a discrete spectrum, they
are not localized and not associated with any anomalies in the transmission.
The ratio of the number of the normal QNMs to the total number of QNMs is
independent of the type of disorder, and slightly deviates from the constant
$\sqrt{2/5}$ in rather large ranges of the strength of a single scattering and
the length of the random sample.
