The success of immersed boundary methods depends on an appropriate treatment of cut elements. While for elliptic problems the question of precise and efficient element integration, stability and convergence is central, immersed transient solvers also need to address possible restrictions of the stability of time stepping schemes. We consider the finite cell method [1] and its extension to wave propagation problems, the spectral cell method (SCM) [2]. In the special case of only interior elements (i.e. a spectral element method with only uncut cells) the mass matrix of the SCM is purely diagonal and thus ideally suited for explicit time integration schemes. Yet, mass matrices of cut elements violate diagonality and, in case of small cuts, may introduce unduly small time step limits. In [2] special lumping schemes for cut cells were introduced, which yet reduce the accuracy of the approximation. We consider in this contribution an alternative approach, an implicit-explicit time integration scheme [3] to exploit the advantages of diagonality for uncut cells on one side and the unconditional stability of implicit time integration for cut cells on the other. In this hybrid, immersed Newmark IMEX approach, we use explicit second-order central differences to integrate the uncut degrees of freedom, leading to a diagonal block in the mass matrix and an implicit trapezoidal Newmark method to integrate the remaining degrees of freedom, with support of at least one cut cell. We discuss algorithmic details and show the accuracy and efficiency of this immersed boundary IMEX approach on several numerical examples. [1] A. Düster, E. Rank, and B. Szabó, “The p-Version of the Finite Element and Finite Cell Methods,”in Encyclopedia of Computational Mechanics Second Edition (E. Stein, R. Borst, and T. Hughes, eds.), pp. 1–35, 2017. [2] M. Joulaian, S. Duczek, U. Gabbert, and A. Düster, “Finite and spectral cell method for wave propagation in heterogeneous materials,” Computational Mechanics, vol. 54, 2014. [3] T. J. R. Hughes and W. K. Liu, “Implicit-explicit finite elements in transient analysis: Implementation and numerical examples,” Journal of Applied Mechanics, Transactions ASME, vol. 45, p. 375 – 378, 1978.