Using fixed point method, we prove the Hyers-Ulam stability of the orthogonally additive functional equation (0.1) $f(2x+y)=2f(x)+f(y)$ and of the orthogonally quadratic functional equation (0.2) $2f(frac{x}{2}+y)+2f(frac{x}{2}-y)=f(x)+4f(y)$ for all $x$, $y$ with $x{perp}y$ in orthogonality spaces.