The electromagnetic fields of a low-frequency horizontal electric dipole placed over a two-layer earth have been derived. The overburden is considered to be transversely isotropic with respect to the conductivity. The unequal principal axis of the conductivity tensor is normal to the layers. The substratum is taken as isotropic. The vector potentials at the surface of the earth have been evaluated and expressed in such a way that the fields may be easily calculated. We have considered the special cases of a perfectly conducting, a perfectly insulating, and a substratum whose conductivity is very close to the longitudinal conductivity of the overburden. Asymptotic expressions for the fields have also been calculated. All the results are given in terms of known functions, and some numerical results have been included.