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In this paper,the necessary and sufficient conditions for general one-step methods to be exponentially fitted at q0∈C are given.A class of multiderivative hybrid one-step methods of order at least s+1 is constructed with s+1 parameters,where s is the order of derivative.The necessary and sufficient conditions for these methods to be A-stable and exponentially fitted is proved.Furthermore,a class of A-stable 2 parameters hybrid one-step methods of order at least 8 are constructed,which use 4th order derivative.These methods are exponentially fitted at q0 if and only if its fitted function f(q) satisfies f(q0)=0.Finally,an A-stable exponentially fitted method of order 8 is obtained.