The brace notation, introduced by Allen and Császár (1993,J. chem. Phys.,982983), provides a simple and compact way to deal with derivatives of arbitrary non-tensorial quantities. One of its main advantages is that it builds the permutational symmetry of the derivatives directly into the formalism. The brace notation is applied to formulate the generalnth-order Cartesian derivatives of internal coordinates, and to provide closed forms for general,nth-order transformation equations of anharmonic force fields, expressed as Taylor series, from internal to Cartesian or normal coordinate spaces.