Quantum mechanical adiabatic approximations describe the small ε behavior of solutions of the Schrödinger equation iϵ αζ αt =H(t)ζ for − T≤ t≤ T. It is well known that if H( t) is analytic in t, self-adjoint for real t, and has an isolated eigenvalue E( t) of multiplicity one for − T≤ t≤ T, then these is a solution that is asymptotic to e − ∫ 0 1 E(r) dr c (φ(t)+ϵζ 1(t)+ϵ 2ζ 2(t)+…) The leading term, Π( t), is a unit vector in the spectral subspace for h( t) that corresponds to E( t). In this paper we investigate eigenvalue crossings. We assume H( t) has two analytic eigenvalues E A ( t) and E B ( t) that are isolated from the rest of the spectrum of H( t). We further assume that E A ( t) and E B ( t) are isolated from one another and are of multiplicity one, except at t=0, where they are equal. We prove that in this situation, the Schrödinger equation has solutions with asymptotic expansions of the form e − ∫ 0 1 E j(r) dr ϵ (φ j(t)+v 1(ϵ)ζ j 1(t,ϵ)+v 2(ϵ)ζ j 2(t,ϵ)+…) (j=A,B) The ψ j k(t, ε) are uniformly bounded for − T≤ t≤ T, and ψ j ( t) is a unit vector in the spectral subspace corresponding to E j ( t). The expansion orders, ν k ( ε), have the form ε n(k) (p+1) (log(ε)) m(k) , where p is the order of the zero of E A ( t)- E B ( t), and n( k) and m( k) are certain non-negative integers.