We consider the Harper equation ψ(x + h) + ψ(x - h) + 2λ cos (2πx)ψ(x) = Eψ(x), x R, where h > 0, 0 < λ ≤ 1, and E ϵ R are parameters. This equation appears as a model in solid state physics and has intriguing spectral properties. In the quasiclassical limit, i.e., as h → 0, we describe the asymptotics of monodromy matrices for the Harper equation. This enables us to get information on the asymptotic structure of the spectrum.