  The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is examined in
quasi-one-dimensional s-wave and d-wave superconductors with particular
attention paid to the effect of the Fermi-surface anisotropy. The upper
critical field $H_{c2}(T)$ is found to exhibit a qualitatively different
behavior depending on the ratio of the hopping energies $t_b/t_a$ and the
direction of the FFLO modulation vector q, where $t_a$ and $t_b$ are the intra-
and interchain hopping energies, respectively. In particular, when $t_b/t_a <
0.1$ and $\mathbf{q} \parallel \mathbf{a}$, we find a novel dimensional
crossover of $H_{c2}(T)$ from one dimension to two dimensions, where a is the
lattice vector of the most conductive chain. Just below the tricritical
temperature $T^*$, the upper critical field $H_{c2}(T)$ increases steeply as in
one-dimensional systems, but when the temperature decreases, the rate of
increase in $H_{c2}(T)$ diminishes and a shoulder appears. Near $T = 0$,
$H_{c2}(T)$ shows a behavior typical of the FFLO state in two-dimensional
systems, i.e., an upturn with a finite field at $T = 0$. When the angle between
$\mathbf{q}$ and $\mathbf{a}$ is large, the upper critical field curve is
convex upward at low temperatures, as in three-dimensional systems, but the
magnitude is much larger than that of a three-dimensional isotropic system. For
$t_b/t_a > 0.15$, the upper critical fields exhibit a two-dimensional behavior,
except for a slight shoulder in the range of $0.2 > t_b/t_a > 0.15$. The upper
critical field is maximum for $\mathbf{q} \parallel \mathbf{a}$ both for s-wave
and d-wave pairings, while it is only slightly larger than the Pauli
paramagnetic limit for $\mathbf{q} \perp \mathbf{a}$. The relevance of the
present results to the organic superconductor ${\rm (TMTSF)_2ClO_4}$ is
discussed.
