We study the instabilities caused by four fermion interactions on algebraic spin liquids. Renormalization group (RG) is used for three types of previously proposed spin liquids on the square lattice: the staggered flux state of SU(2) spin system, the π−flux state of SU(4) spin system, and the π−flux state of SU(2) spin system. The low energy field theories of the first two types of spin liquids are QED3 with emerged SU(4) and SU(8) flavor symmetries , the low energy theory of the π−flux SU(2) spin liquid is the QCD3 with SU(2) gauge field and emergent Sp(4) (SO (5)) flavor symmetry. Suitable large-N generalization of these spin liquids are discussed, and a systematic 1/N expansion is applied to the RG calculations. The most relevant four fermion perturbations are identified, and the possible phases driven by relevant perturbations are discussed.