In 1980 and 1986, Nedelec proposed H(curl)-conforming elements to solve electromagnetic equations that contain the "curl" operator. It is more or less as the H^1-conforming elements (or C^0 elements) for elliptic equations that contain the "grad" operator. As is well known in the finite element method literature, in order to solve 4th-order elliptic equations such as the bi-harmonic equation, H^2-conforming elements (or C^1-elements) were developed. Recently, there has been some research in solving electromagnetic equations which involve four "curl" operators. Hence, construction of H(curl curl)-conforming elements becomes necessary. In this work, we construct H(curl curl)-conforming elements for rectangular and triangular meshes and apply them to solve quad-curl equations as well as related eigenvalue problems. Speaker(s): Zhimin Zhang (Wayne State University)