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In this paper, $f(R,T,R_{\mu\nu} T^{\mu\nu}$) gravity is considered. It is amodified theory of gravity that exhibits a strong coupling of gravitational andmatter fields. Therefore, if gravity is governed by this model a number ofissues must be re-examined. In this context, the question of causality and itsviolation is studied. Such analysis is carried out using the G\"{o}del-typesolutions. It is shown that this model allows both causal and non-causalsolutions. These solutions depend directly on the content of matter present inthe universe. For the non-causal solution, a critical radius is calculated,beyond which causality is violated. Taking different matter contents, aninfinite critical radius emerges that leads to a causal solution. In thiscausal solution, a natural relationship emerges between the parameters thatdetermine the matter considered.

G\"{o}del-type solutions in $f(R,T,R_{\mu\nu} T^{\mu\nu}$) gravity