Let $(X,J,\omega,\Omega)$ be a Calabi–Yau $m$-fold, and $N$ a compact special Lagrangian $m$-fold in $X$. Suppose $(X,\tilde{J},\tilde{\omega},\tilde{\Omega})$ is a nearby Calabi–Yau structure on $X$. Provided $(X,\tilde{J},\tilde{\omega},\tilde{\Omega})$ is sufficiently close to $(X,J,\omega,\Omega)$, there exists a special Lagrangian $m$-fold $\tilde{N}$ in $(X,\tilde{J},\tilde{\omega},\tilde{\Omega})$ close to $N$ in $X$ if and only if $[\tilde{\omega}|_{N}]=0$ in $H^{2}(N,\mathbin{\mathbb{R}})$ and $[\mathop{\rm Im}\tilde{\Omega}|_{N}]=0$ in $H^{m}(N,\mathbin{\mathbb{R}})$.