Developments In Numerical Initial Value Ode Methods Were The Focal Topic Of The Meeting At L'aquila Which Explord The Connections Between The Classical Background And New Research Areas Such As Differental-algebraic Equations, Delay Integral And Integro-differential Equations, Stability Properties, Continuous Extensions (interpolants For Runge-kutta Methods And Their Applications, Effective Stepsize Control, Parallel Algorithms For Small- And Large-scale Parallel Architectures). The Resulting Proceedings Address Many Of These Topics In Both Research And Survey Papers. Contents: C. Baiocchi: Stability In Linear Abstract Differential Equations -- A. Bellen: Parallelism Across The Steps For Difference And Differential Equations -- D. Di Lena, D. Trigiante: On The Spectrum Of Families Of Matrices With Applications To Stability Problems -- C.w. Gear: Daes: Odes With Constraints And Invariants -- P.j. Van Der Houwen, B.p. Sommeijer, G. Pontrelli: A Comparative Study Of Chebyshev Acceleration And Residue Smoothing In The Solution Of Nonlinear Elliptic Difference Equations -- O. Nevanlinna: A Note On Picard-lindelΓΆf Iteration -- S.p. Norsett, H.h. Simonsen: Aspects Of Parallel Runge-kutta Methods -- L.f. Shampine: Tolerance Proportionality In Ode Codes. A. Bellen, C.w. Gear, E. Russo (eds.). Includes Bibliographical References.