<p><b>Abstract</b>—In [<ref type="bib" rid="biT136910">10</ref>], Sengupta and Dahbura discussed how to characterize a diagnosable system under the comparison diagnosis model proposed by Maeng and Malek [<ref type="bib" rid="biT13697">7</ref>] and a polynomial algorithm was given to identify the faulty processors provided that the system's diagnosability is known. However, for a general system, the determination of its diagnosability is not algorithmically easy. This paper proves that, for the important hypercube-structured multiprocessor systems (<tmath>$n$</tmath>-cubes), the diagnosability under the comparison model is <tmath>$n$</tmath> when <tmath>$n\geq 5$</tmath>. The paper also studies the diagnosability of enhanced hypercube [<ref type="bib" rid="biT136911">11</ref>], which is obtained by adding <tmath>$2^{n-1}$</tmath> more links to a regular hypercube of <tmath>$2^{n}$</tmath> processors. It is shown that the augmented communication ability among processors also increases the system's diagnosability under the comparison model. We will prove that the diagnosability is <tmath>$n+1$</tmath> for an enhanced hypercube when <tmath>$n\geq 6$</tmath>.</p>