Black Box
Black box methods may be able to identify evidence of race conditions via methods such as multiple simultaneous connections, which may cause the software to become instable or crash. However, race conditions with very narrow timing windows would not be detectable.
White Box
Common idioms are detectable in white box analysis, such as time-of-check-time-of-use (TOCTOU) file operations (CWE-367), or double-checked locking (CWE-609).