High-order-accurate implicit time-marching methods are presented for discontinuous Galerkin and spectral volume high-order-accurate spatial discretizations of the linearized Euler equations that govern propagation of aeroacoustic disturbances. It is found that despite the additional computational time that is required for the solution of the large, sparse linear system for the degrees of freedom of high-order spectral volume or discontinuous Galerkin discretizations, implicit methods offer an attractive alternative for practical aeroacoustic computations with these high-order methods. Several explicit and implicit methods for time advancement are tested. The advantages of implicit higher-order-accurate (in time) methods that involve multiple implicit steps are demonstrated. The efficiency and accuracy of time-marching methods is evaluated for test problems with exact solutions. It is shown that complex domain aeroacoustic predictions can be obtained at a reduced computational cost with the use of high-order-accurate implicit methods.