Soit $\{(Y_{\bf i},{\bf X_{{\bfi}} }), {\bf i}\in\mathbbZ^N\}$ un processus spatial stationnaire de dimension $(d+1)$. On note ${\bf x}\mapsto q_p({\bf x}) $, $p\in (0,1)$, ${\bf x}\in{\mathbb R} ^d$, la fonction de r\' egression quantile spatiale d'ordre $p$, caracteris\' ee par ${\rm P}\{Y_{{\bfi}} \leq q_p({\bfx})\vert {\bf X_{{\bfi}} }= {\bf x }\}=p$. On suppose que le processus a \' et\' e observ\' e sur un domaine spatial rectangulaire $N$-dimensionnel, de la forme ${\cal I}_{\bf n}:=\{ {\bf i}=(i_1,\ldots , i_N)\in{\mathbb Z}^N\vert 1\leq i_k \leq n_k, \, k=1,\ldots , N\}$, où ${\bf n}=(n_1,\ldots , n_N)\in{\mathbb Z}^N$. Nous proposons un estimateur localement lin\' eaire de $ q_p$, g\' en\' eralisant aux champs al\' eatoires avec d\' ependance spatiale complexe et non sp\' ecifi\' ee les m\' ethodes de r\' egression quantile consid\' er\' ees dans le contexte des observations ind\' ependantes ou des s\' eries temporelles. Sous des conditions tr\` es g\' en\' erales, nous obtenons une repr\' esentation de Bahadur pour les estimateurs de $q_p$ et de ses d\' eriv\' ees premières, à partir de laquelle nous \' etablissons leur convergence et leur normalit\' e asymptotique. Le processus spatial est soumis à des hypothèses de m\' elange qui g\' en\' eralisent les concepts chronologiques habituels. La taille du domaine rectngulaire ${\cal I}_{\bf n}$ peut tendre vers l'infini selon des taux non isotropes. La m\' ethode fournit sur la d\' ependance entre $Y$ et les r\' egresseurs ${\bf X}$ des renseignements beaucoup plus riches que les traditionnelles m\' ethodes de r\' egression lin\' eaire g\' en\' eralement adopt\' ees dans le domaine de la mod\' elisation spatiale. \vspace3mm Ce travail a \' et\' e r\' ealis\' e en collaboration avec Zudi {\sc Lu} (University of Adelaide) et Keming {\sc Yu} (Brunel University). Mots-cl\' es : Champs al\' eatoires, R\' egression quantile, repr\' esentation de Bahadur, Estimation localement lin\' eaire.\vspace5mm \noindent{\sc R\' ef\' erences}\vspace2mm \noindent Hallin, M., Lu, Z. and Yu, K. (2009). Local linear spatial quantile regression. {\it Bernoulli} {\bf 15}, 659-686. \vspace5mm \begincenter {{\sc Local Linear Spatial Quantile Regression} } \endcenter Let $\{(Y_{\bf i},{\bf X_{{\bfi}} }), {\bf i}\in\mathbbZ^N\}$ be a stationary real-valued $(d+1)$-di\-men\-sional spatial process. Denote by ${\bf x}\mapsto q_p({\bf x}) $, $p\in (0,1)$, ${\bf x}\in{\mathbb R} ^d$, the spatial quantile regression function of order $p$, characterized by ${\rm P}\{Y_{{\bfi}} \leq q_p({\bfx})\vert {\bf X_{{\bfi}} }= {\bf x }\}=p$. Assume that the process has been observed over an $N$-dimensional rectangular domain of the form ${\cal I}_{\bf n}:=\{ {\bf i}=(i_1,\ldots , i_N)\in{\mathbb Z}^N\vert 1\leq i_k \leq n_k, \, k=1,\ldots , N\}$, with ${\bf n}=(n_1,\ldots , n_N)\in{\mathbb Z}^N$. We propose a local linear estimator of $ q_p$ extending to random fields with unspecified and possibly highly complex spatial dependence structure the quantile regression methods considered in the context of independent samples or time series. Under mild regularity assumptions, we obtain a Bahadur representation for the estimators of $q_p$ and its first order derivatives, from which we establish consistency and asymptotic normality. The spatial process is assumed to satisfy general mixing conditions, generalizing classical time-series mixing concepts. The size of the rectangular domain ${\cal I}_{\bf n}$ is allowed to tend to infinity at different rates depending on the direction in ${\mathbb Z}^N$ (non-isotropic asymptotics). The method provides much richer information than the mean regression approach considered in most spatial modelling techniques.