According to the parallel architecture, syntactic and semantic information processing are two separate streams that interact selectively during language comprehension. While considerable effort is put into psycho‐ and neurolinguistics to understand the interchange of processing mechanisms in human comprehension, the nature of this interaction in recent neural Large Language Models remains elusive. In this article, we revisit influential linguistic and behavioral experiments and evaluate the ability of a large language model, GPT‐3, to perform these tasks. The model can solve semantic tasks autonomously from syntactic realization in a manner that resembles human behavior. However, the outcomes present a complex and variegated picture, leaving open the question of how Language Models could learn structured conceptual representations.