Interchain hopping in systems of coupled chains of correlated electron
s is investigated by exact diagonalization and quantum Monte Carlo met
hods. For two weakly coupled Hubbard chains at commensurate densities
(e.g., n=1/3), the spitting at the Fermi level between bonding and ant
ibonding bands is strongly reduced (but not suppressed) by repulsive i
nteractions extending to a few lattice spacings. The magnitude of this
reduction is directly connected to the exponent ct of the one-dimensi
onal Luttinger liquid. However, we show that the incoherent part of th
e single-particle spectral function is much less affected by the inter
chain coupling. This suggests that incoherent interchain hopping could
occur for intermediate alpha values.