Thispaperdealswiththenumericalsolutionofinitialvalueproblemsforpantographdifferentialequationswithvariabledelays.Weinvestigatethestabilityofonelegθ-methodsinthenumericalsolutionoftheseproblems.Sufficientconditionsfortheasymptoticstabilityofθ-methodsaregivenbyFourieranalysisandErgodictheory.