A new kind of attribute grammars, called higher order attribute grammars, is defined. In higher order attribute grammars the structure tree can be expanded as a result of attribute computation. A structure tree may be stored in an attribute. The term higher order is used because of the analogy with higher order functions, where a function can be the result or parameter of another function. A relatively simple method, using OAGs, is described to derive an evaluation order on the defining attribute occurrences which comprises all possible direct and indirect attribute dependencies. As in OAGs, visit-sequences are computed from which an efficient algorithm for attribute evaluation can be derived.