Asymptotic Properties for Increments of $l^{\infty}$-Valued Gaussian Random Fields This paper establishes general theorems which contain both moduli of continuity and large incremental results for $l^\infty$-valued Gaussian random fields indexed by a multidimensional parameter under explicit conditions. Keywords:$l^\infty$-valued Gaussian random field, modulus of continuity, regularly varying function, large deviation probabilityCategories:60F15, 60G15, 60G60