  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.
