Stability condition for an iir filter
For a causal system to be stable, all the poles have to be inside the unit circle. In general, they may be complex, although they always come in complex conjugate pairs in order to keep the output real for real inputs.

So, the answer is no, there are no extra requirements for the poles to be on the real axis. However, they must be complex conjugates for the output to be real for a real input.

I would like to point out that the region of convergence of the Z Transform may include the unit circle, and yet the system may be non causal (but stable). For example, consider the impulse response: $h[n] = -a^{n}u[-n-1]$, for $|a| &gt; 1$, which corresponds to a system having a pole outside the unit circle, and yet it is a stable (although non-causal) system.