A series of III-V-based magnetic semiconductor heterostructures, p-type (In,Mn)As/ (Ga,Al)Sb, has been grown by molecular beam epitaxy. Studies on magnetotransport and magneto-optical properties show that perpendicular ferromagnetic order occurs in the heterostructures with thin (In,Mn) As layers. The origin is discussed in terms of both carrierand strain-induced effects. (In,Mn)As is a new III-V-based diluted magnetic semiconductor with interesting properties associated with carrier-induced magnetism. It has been shown that the spin exchange between holes and Mn ions in p-type Int-#n+s (x=0.014.02) films causes an anomalous Hall effect over a wide temperature range (1.6-200 K). Carrier-induced partial ferromagnetic order is observed below 10 K.' In this letter, we report on the striking ferromagnetic order, accompanied by a strong perpendicular anisotropy, in p-(In,Mn) As/(Ga,Al) Sb heterostructures with thin (5-30 nm) p-(In,Mn)As layers. These heterostructures were grown by molecular beam epitaxy (MBE). The appearance of perpendicular ferromagnetic order as a function of (In,Mn)As thickness is demonstrated by lowfield Hall measurements, while the hole concentration and mobility are extracted from high-field magnetotransport data. Magneto-optical properties are examined by polar Kerr rotation experiments, through which we show that the rotation is relatively large (0.1-0.2") and has complex wavelength and thickness dependencies. On the basis of the dependencies of ferromagnetic behavior on (In,Mn)As thickness and GaSb-based buffer alloy composition, we propose that the observed perpendicular ferromagnetic order results from the combination of carrier-induced and magnetoelastic effects, in biaxially strained (In,Mn)As layers. We grew (In,Mn)As/(Ga,Al) (Sb,As)/GaSb/GaAs structures on GaAs(100) substrates, with the thickness of each constituent layer ranging from 3nm to 1 pm, 0.13-0.3 pm, 0.3-1.2 ,um, and 0.3 ,um, from the top (In,Mn)As to the bottom GaAs buffer, respectively. Here, the (Ga,Al) (Sb,As) indicates either binary GaSb or AlSb compounds, or ternary (Ga,Al)Sb or Al(Sb,As) alloys. Mn fraction x in the In,-,Mn& layer ranged between 0.04 and 0.15. The substrate temperature T, for the growth of nonmagnetic III-V layers was T,=480-580 "C, whereas T,= 170-200 "C for the (In,Mn)As layers. The low-T, growth yields a homogeneous (In,Mn)As film in the zincblende structure without the macroscopic ferromagnetic MnAs second phase, as confirmed recently by transmission electron diffraction studies for thick (> 2 pm>