  Let $R_s(n)$ denote the number of representations of the positive number $n$
as the sum of two squares and $s$ biquadrates. When $s=3$ or $4$, it is
established that the anticipated asymptotic formula for $R_s(n)$ holds for all
$n\le X$ with at most $O(X^{(9-2s)/8+\varepsilon})$ exceptions.
