Sentences where two verbs share a single argument represent a complex and highly ambiguous syntactic phenomenon. The argument sharing relations must be considered during the detection process from both a syntactic and semantic perspective. Such expressions can represent ungrammatical constructions, denoted as zeugma, or idiomatic elliptical phrase combinations. Rule-based classification methods prove ineffective because of the necessity to reflect meaning relations of the analyzed sentence constituents.||||This paper presents the development and evaluation of ZeugBERT, a language model tuned for the sentence classification task using a pre-trained Czech transformer model for language representation. The model was trained with a newly prepared dataset, which is also published with this paper, of 7849 Czech sentences to classify Czech syntactic structures containing coordinated verbs that share a valency argument (or an optional adjunct) in the context of coordination. ZeugBERT here reaches 88% of test set accuracy. The text describes the process of the new dataset creation and annotation, and it offers a detailed error analysis of the developed classification model.