In this talk we discuss a quasilinear system involving the curl operator, which describes the Meissner state of anisotropic superconductors. In the case of isotropic superconductors, this problem has been studied by many physicists and mathematicians. Following the previous work jointly with Peter Bates with necessary change, we prove the existence and regularity of the weak solutions, and the asymptotic behavior of the solutions with small penetration depth. The existence of solutions is proved by applying variational method to a modified system.