We report time resolved measurements of spin relaxation in doped and undoped InSb quantum wells using degenerate and two-color magneto-optical Kerr effect techniques. We observed that the photo-excited spin dynamics are strongly influenced by laser excitation fluence and the doping profile of the samples. In the low fluence regime, an oscillatory pattern was observed at low temperatures ($leq$ 77 K) in the samples with an asymmetric doping profile which might be attributed to the quasi-collision-free spin relaxation regime. Our measurements also suggest the influence of the barrier materials (Al$_{x}$In$_{1-x}$Sb) on the spin relaxation in these material systems.
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