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This study investigates delay-dependent stability of a class of highly non-linear stochastic functional differential equations with Markovian switching. Some novel boundedness and stability criteria are first established, including H∞ stability in Lp, asymptotic stability in Lp and almost surely asymptotic stability, based on Lyapunov functions and generalised Itô formula. Concretely, the authors generalise and improve the existing results to the hybrid stochastic functional differential equations case. An example is presented to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]