Two-loop next-to-leading m$_{t}$ corrections to the $\varrho$ parameter

The O(G^2_\mu m_t^4) correction to the \rho parameter is computed within the Standard Model using the current algebra formulation of radiative corrections. This approach is proved to be equivalent to the effective Lagrangian method proposed by Barbieri {\em et al.} Using the same framework, the O(G^2_\mu m_t^2 m_z^2) correction to the ratio of neutral-to-charged current amplitudes is analysed in an SU(2) model. The O(G^2_\mu m_t^2 m_z^2) contribution is shown to be numerically comparable to the leading O(G^2_\mu m_t^4) term for realistic values of the top mass. The resummation of higher-order effects is discussed.