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A scheme suitable for describing quantum nonultralocal models includingsupersymmetric ones is proposed. Braided algebras are generalised to be usedthrough Baxterisation for constructing braided quantum Yang--Baxter equations.Supersymmetric and some known nonultralocal models are derived in the frameworkof the present approach. As further applications of this scheme construction ofnew quantum integrable nonultralocal models like mKdV and anyonicsupersymmetric models including deformed anyonic super algebra are outlined.Comment: 23 pages (Latex), replaced by extended published versio

QUANTUM INTEGRABILITY OF NON-ULTRALOCAL MODELS THROUGH BAXTERIZATION OF QUANTIZED BRAIDED ALGEBRA