  We study the time dynamics of the ohmic spin boson model at arbitrary bias
$\epsilon$ and small coupling $\alpha$ to the bosonic bath. Using perturbation
theory and the real-time renormalization group (RG) method we present a
consistent zero-temperature weak-coupling expansion for the time evolution of
the reduced density matrix one order beyond the Bloch-Redfield solution. We
develop a renormalized perturbation theory and present an analytical solution
covering the whole range from small to large times, including further results
for exponentially small or large times. Resumming all secular terms in all
orders of perturbation theory we find exponential decay for all terms of the
time evolution. We determine the preexponential functions and find slowly
varying logarithmic terms with the renormalized Rabi frequency $\Omega$ as
energy scale together with strongly varying parts falling off asymptocially as
$1/t$ in leading order, in contrast to the unbiased case. Resumming all
logarithmic terms in all orders of perturbation theory via real-time RG we find
the correct renormalized tunneling and a power-law behaviour for the
oscillating modes with exponent crossing over from $2\alpha$ for exponentially
small times to a bias-dependent value $2\alpha \epsilon^2/\Omega^2$ for
exponentially large times. Furthermore, we present a degenerate perturbation
theory to calculate consistently the purely decaying mode one order beyond
Bloch-Redfield.
