Abstract: One of the most promising concepts which has been developed for efficient representation of Boolean functions is Linearly Transformed Binary Decision Diagram (LTBDD). We present extensions to LTBDDs called Function-driven Decision Diagrams (fDDs). The notion of fDDs is based on using simple balanced (including nonlinear) Boolean functions for defining transformations of decision diagrams. In this context a new scheme of preprocessing which corresponds to inverse transformations as well as using composition of transformations are very efficient for minimization of fDDs. The first experimental results show that fDDs driven by nonlinear Boolean functions can be more compact than LTBDDs, with a reasonable cost. Further extensions of fDDs are also mentioned such as Function-driven Kronecker Functional Decision Diagrams and Multiple-Valued Function-driven Decision Diagrams.