In [5] a fuzzy topology on a set $X$ was defined as a fuzzy subset $\tau$ of the family $I^x$ of fuzzy subsets of $X$ $(\tau:I^x\to I)$ satisfying some axioms. In this paper the notions of a neighborhood structure and of a $q$-neighborhood structure are introduced and studied. These structures are applied to obtain local description of fuzzy topological spaces. As a special case the obtained theory contains in itself the local theory of Chang fuzzy spaces developed by Pu and Liu [3].