Optimized high-order compact(OHOC) schemes, proposed to simulate the aero-acoustic problems due to unsteady compressible flows, have high spatial order of truncation and resolution. To solve wave or Euler equations, explicit time marching schemes are employed in general for the OHOC because of the simplicity of the schemes. In this research, implicit OHOC scheme is developed, which results in block hepta-diagonal matrix. This thesis presents the results of Von-Neumann stability analysis of the implicit formulations which have 1st, 2nd, 3rd, and 4th-order of time accuracy. The analysis shows that the 1st is unconditionally stable, the 2nd is neutrally stable, the 3rd is conditionally stable and the 4th-order is unconditionally unstable. One dimensional wave problem is solved with the 2nd order scheme and the result is campared with one obtained by using the explicit scheme having the same order. Explicit scheme is unstable with C.F.L. number 0.5, whereas the implicit scheme is stable with C.F.L. number 1. One dimensional nonlinear shock wave is solved with 1st order scheme and the results are compared with exact values, which show reasonable solutions. The acoustic fields driven by baffled piston in 2-dimension, are computed with the 2nd order scheme. By comaparing with the exact solution, the result is stable but shows large dissipations. It can be concluded that the low order implicit schemes are stable and can be used for steady solutions but further development of the stable high order implicit scheme is necessary for unsteady solutions.