For system diagnosis, Lai et al.16 introduced a new measurement, called the conditional diagnosability, by adding a condition that no faulty set contains all the neighbors of any vertex in a network. Taking the hypercube as the target, Lai et al.16 (respectively, Hsu et al.13) estimated the PMC-based19 (respectively, the comparison-based18) conditional diagnosability as about four (respectively, three) times larger than the original diagnosability. In this paper, we extend the concept of conditional diagnosability to the generalized version of hypercubes, the class of hypercube-like networks. We prove that the conditional diagnosability of an n-dimensional hypercube-like network HLn is 3n - 5 under the comparison diagnosis model, for n ≥ 5. [ABSTRACT FROM AUTHOR]