Eluh is the Assistant Police Commissioner (Crimes) and Gitua is the Assistant Director for the National Fraud and Anti-Corruption Directorate.
Acting Judge Leka Nablu granted leave for both officers, ordering that they file a notice of motion within seven days from today (30 Oct).
She ordered the matter return for inter-parties hearing on November 5 while the stay on their termination has also been extended to next Friday.
The matter will also go on the fast track list for it to be dealt with quickly.
Judge Nablu in granting leave said both officers had an arguable case and it was inappropriate to have the Police Commissioner review his own decision.
She said it was only proper it comes before the National Court for judicial review.
Eluh and Gitua were terminated on the 23rd and 28th of September respectively.
That termination was stayed on October 8 and has been further extended to November 5.