A hybrid implicit-explicit scheme is developed for Eulerian hydrodynamics. The hybridi~atlon is a continuous switch and operates on each characteristic field separately. The explicit scheme is a version of the second-order Godunov scheme; the implicit method is only firstorder accurate in time but leads to Ii block tridiagonal matrix inversion for efficiency and is unconditionally stable for the case of linear advection. The methodology is described for the cases of linear advection, for

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... ar scalar problems, and for gas dynamics. An important element of our work is the use of a modified Engquist-osher flux function In place of the Godunov flux. Several numerical results are presented to demonstrate the properties of the method, especially stable numerical shocks at very high CFL numbers and second-order accurate steady states. Cl