We investigate theoretically the identification of the external-cavity roundtrip time of an external-cavity semiconductor laser (ECSL). The time-delay identification is performed by analyzing the laser-intensity time series with conventional techniques based on the autocorrelation function or mutual information. We find that a weak feedback rate and a time-delay close to the laser's intrinsic relaxation-oscillation period are two conditions leading to difficult delay identification. This arduous time-delay identification is of particular interest for the security improvement of chaos-based communications schemes using ECSLs.