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We theoretically study the orbital destructive effect againstsuperconductivity in a parallel magnetic field in theFulde-Ferrell-Larkin-Ovchinnikov (FFLO or LOFF) phase at zero temperature in aquasi-two-dimensional (Q2D) conductor. We demonstrate that at zero temperaturea special parameter, $\lambda = l_{\perp}(H)/d$, is responsible for strength ofthe orbital effect, where $l_{\perp}(H)$ is a typical "size" of thequasi-classical electron orbit in a magnetic field and $d$ is the inter-planedistance. We discuss applications of our results to the existing experiments onthe FFLO phase in the organic Q2D conductors $\kappa$-(ET)$_2$Cu(NCS)$_2$ and$\kappa$-(ET)$_2$Cu[N(CN)$_2$]Cl.

Orbital Effect for the Fulde-Ferrell-Larkin-Ovchinnikov Phase in a Quasi-Two-Dimensional Superconductor in a Parallel Magnetic Field