  A local linear kernel estimator of the regression function x\mapsto
g(x):=E[Y_i|X_i=x], x\in R^d, of a stationary (d+1)-dimensional spatial process
{(Y_i,X_i),i\in Z^N} observed over a rectangular domain of the form
I_n:={i=(i_1,...,i_N)\in Z^N| 1\leq i_k\leq n_k,k=1,...,N}, n=(n_1,...,n_N)\in
Z^N, is proposed and investigated. Under mild regularity assumptions,
asymptotic normality of the estimators of g(x) and its derivatives is
established. Appropriate choices of the bandwidths are proposed. The spatial
process is assumed to satisfy some very general mixing conditions, generalizing
classical time-series strong mixing concepts. The size of the rectangular
domain I_n is allowed to tend to infinity at different rates depending on the
direction in Z^N.
