This paper explores local absolute instability in the boundary layer flow over two distinct families of rotating

spheroids (prolate and oblate). While convective instability was established in earlier work by Samad and

Garrett [1], this study delves into the potential occurrence of local absolute instability. Some results of local

convective instability under the assumption of stationary vortices are reproduced for a more comprehensive

investigation. The analysis considers viscous and streamline curvature effects, demonstrating that the localized

mean flow within the boundary layer over either family of the rotating spheroid is absolutely unstable for each

fixed value of the eccentricity parameter ???? ∈ [0, 0.8]. For certain combinations of Reynolds number ???????? and

azimuthal wave number ????, a third branch (Branch 3) of the dispersion relation intersects Branch 1 at a pinch

point, indicating absolute instability. Neutral curves depict regions that are absolutely unstable, while below

critical Reynolds numbers, the region is either convectively unstable or stable. The paper also illustrates the

effect of increasing eccentricity on spatial branches within both convectively and absolutely unstable regions.

From lower to moderate latitudes, the stabilizing effect of ???? on the onset of absolute instability is robust for

the prolate family and almost negligible for the oblate family. At high latitudes of the prolate spheroid, the

stabilizing effect of ???? is fainter but persists until close to the equator. Conversely, at high latitudes of the oblate

spheroid, the stabilizing effect of ???? is more pronounced. The paper discusses the implications of the parallel

flow assumption employed in the analyses.