2. Given the function $f(x)=\frac{\sqrt{a^{2}-x^{2}}}{|x+a|-a}$ is an odd function, then the range of values for $a$ is
2. $a>0$.

Necessity. If $f(x)=\frac{\sqrt{a^{2}-x^{2}}}{|x+a|-a}$ is an odd function, then since $y=\sqrt{a^{2}-x^{2}}$ is an even function, it follows that $y=|x+a|-a$ is an odd function. Therefore, $|-x+a|-a=-(|x+a|-a)$, which means $|x+a|+|x-a|=2a$ holds for all $x$ in the domain. Hence, $a>0$.
Sufficiency. If $a>0$, then the domain of $f(x)$ is $[-a, 0) \cup (0, a]$. In this case, $f(x)=\frac{\sqrt{a^{2}-x^{2}}}{x}$ is clearly an odd function.