  In this paper we give a classification of tilings of the sphere by congruent
quadrilaterals with exactly two equal edges. The tilings are the earth map
tilings, $(p,q)$-earth map tilings and their flip modifications, and
quadrilateral subdivisions of the cube and the triangular prism. We described
the ranges of values of the edges and angles for the tile to be geometrically
realisable. The symmetry groups of the tilings are also determined.
