AbstractA new representation for diagonally implicit multistage integration methods (DIMSIMs)is derived in which the vector of external stages directly approximates the Nordsieckvector. The methods in this formulation are zero-stable for any choice of variable mesh.They are also easy to implement since changing step-size corresponds to a simple rescalingof the vector of external approximations. Finally, we furnish examples of DIMSIMs oforder p=3 and stage order q= p, with an analysis of local truncation error and of erroraccumulation in a variable step-size situation.Keywords: DIMSIM methods, Nordsieck representation, variable step-size, error accumulation,error estimation