The advancement of Large Language Models (LLMs) has significantly impacted biomedical Natural Language Processing (NLP), enhancing tasks such as named entity recognition, relation extraction, event extraction, and text classification. In this context, the DeepSeek series of models have shown promising potential in general NLP tasks, yet their capabilities in the biomedical domain remain underexplored. This study evaluates multiple DeepSeek models (Distilled-DeepSeek-R1 series and Deepseek-LLMs) across four key biomedical NLP tasks using 12 datasets, benchmarking them against state-of-the-art alternatives (Llama3-8B, Qwen2.5-7B, Mistral-7B, Phi-4-14B, Gemma-2-9B). Our results reveal that while DeepSeek models perform competitively in named entity recognition and text classification, challenges persist in event and relation extraction due to precision-recall trade-offs. We provide task-specific model recommendations and highlight future research directions. This evaluation underscores the strengths and limitations of DeepSeek models in biomedical NLP, guiding their future deployment and optimization.