  We prove modularity of some two dimensional, 2-adic Galois representations
over totally real fields that are nearly ordinary and that are residually
dihedral. We do this by employing the strategy of Skinner and Wiles, using Hida
families, together with the 2-adic patching method of Khare and Wintenberger.
As an application we deduce modularity of some elliptic curves over totally
real fields that have good ordinary or multiplicative reduction at places above
2.
