The pure rotational spectra of the alkali bromides and the alkali iodides were investigated in the 1.5 to 5.0 mm range of the microwave region. The experiment was performed by passing a beam of molecules in the vapor state from an oven, capable of producing temperatures up to 1000°C, into an oversized section of wave guide so that the direction of incident microwave radiation was at right angles to the flow direction of the molecular beam. In this way linewidths less than 100 kc/sec at 100 000 Mc/sec were easily achieved. The line frequencies were measured with a precision better than one part in 106. The apparatus was developed as a series of modifications on an earlier experiment performed at this laboratory. Dunham's theory for diatomic molecules was applied in interpretation of the data. In most cases, the values for Be, αe, and γe were known although less accurately, but De and βe were found for the first time. From the latter two, accurate determinations were made for the first time of ωe and ωexe. From these values, information has been obtained about the potential functions, which suitably describe these diatomic alkali halides. In addition, centrifugal distortion constants, isotope mass ratios, moments of inertia, and internuclear distances have been accurately evaluated for each molecule.