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Memory Editing (ME) has emerged as an efficient method to modify erroneous facts or inject new facts into Large Language Models (LLMs). Two mainstream ME methods exist: parameter-modifying ME and parameter-preserving ME (integrating extra modules while preserving original parameters). Regrettably, previous studies on ME evaluation have two critical limitations: (i) evaluating LLMs with single edit only, neglecting the need for continuous editing, and (ii) evaluations focusing solely on basic factual triples, overlooking broader LLM capabilities like logical reasoning and reading understanding. This study addresses these limitations with contributions threefold: (i) We explore how ME affects a wide range of fundamental capabilities of LLMs under sequential editing. Experimental results reveal an intriguing phenomenon: Most parameter-modifying ME consistently degrade performance across all tasks after a few sequential edits. In contrast, parameter-preserving ME effectively maintains LLMs’ fundamental capabilities but struggles to accurately recall edited knowledge presented in a different format. (ii) We extend our evaluation to different editing settings, such as layers to edit, model size, instruction tuning, etc. Experimental findings indicate several strategies that can potentially mitigate the adverse effects of ME. (iii) We further explain why parameter-modifying damages LLMs from three dimensions: parameter changes after editing, language modeling capability, and the in-context learning capability. Our in-depth study advocates more careful use of ME in real-world scenarios.