Vázquez Monzón, CarlosDocobo Durántez, José Ángel2023-07-072023-07-072023Monzón, C.V., Docobo, J.A. Long-term perturbations in four-body systems with mutual highly inclined orbits. Astrophys Space Sci 368, 42 (2023). https://doi.org/10.1007/s10509-023-04200-70004-640Xhttp://hdl.handle.net/10347/30847Hierarchical Three Body systems with mutual highly inclined orbits have been well-known since the 1960s. Lidov-Kozai cycles arise within them where the inner orbit eccentricity acquires extreme values. In particular, we focus our research on the motion of exoplanets and exomoons on different Three Body stellar scenarios. Our goal is to study how the LK cycles are perturbed by a fourth body (which we called perturbed LK). We analyze the evolution of the eccentricity and inclination of the inner orbit in two cases: the first involves an exoplanet and the second involves an exomoon. Due to the possible stable configurations of a four-body system, we treat two subcases as well: the Totally Hierarchical Configuration and the 2 + 2 configuration. According to that derived from the particular scenarios of study discussed in the present research, the LK perturbed in exomoon orbits around exoplanets seem to exhibit, in general, way less alterations than the exoplanet orbit around its stareng© The Author(s) 2023, corrected publication 2023. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ Atribución 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/Celestial mechanicsjournal article10.1007/s10509-023-04200-71572-946Xopen access