  As it is well known there may arise situations when an interaction between
electrons is attractive. A weak attraction should manifest itself strongly in
1D systems, since it can create two-electron bound states. This paper
interprets the 0.7 $(2e^2/h)$ conductance structure, observed recently in a
one-dimensional constriction, as a manifestation of two-electron bound states
formed in a barrier saddle-point. The value 0.75 $(2e^2/h)$ follows naturally
from the 3:1 triplet-singlet statistical weight ratio for the two-electron
bound states, if the triplet energy is lower. Furthermore, the value 0.75 has
to be multiplied by the probability T of the bound state formation during
adiabatic transmission of two electrons into 1D channel ($T\simeq 1$). If the
binding energy is larger than the sub-band energy spacing the 0.7 structure can
be seen even when the integer steps are smeared away by the temperature. Bound
states of several electrons, if they exist, may give different steps at 1/2,
5/16, 3/16 etc in the conductance. The latter results are sensitive to the
length of 1D system and the electron density at the barrier. It is not excluded
that the fractional conductance quantization may also appear for a repulsive
interaction between electrons. In this case the electron level splitting is due
to the exchange interaction with two nearest neighbors in a 1D Wigner crystal.
