Recently, fine-tuning language models pre-trained on large text corpora have provided huge improvements on vision-and-language (V&L) tasks as well as on pure language tasks. However, fine-tuning the entire parameter set of pre-trained models becomes impractical since the model size is growing rapidly. Hence, in this paper, we introduce adapter-based parameter-efficient transfer learning techniques to V&L models such as VL-BART and VL-T5. We evaluate our methods in a unified multi-task setup on four diverse V&L tasks: VQAv2, GQA, NLVR 2 , and MSCOCO image captioning. With careful training and thorough experiments, we benchmark three popular adapter-based methods (Adapter, Hyperformer, Compacter) against the standard full fine-tuning and the recently proposed prompttuning approach. We also enhance the efficiency and performance of adapters by sharing their weights to attain knowledge across tasks. Our results demonstrate that training the adapter with the weight-sharing technique (4.4% of total parameters) can match the performance of fine-tuning the entire model. Lastly, we present a comprehensive analysis including the combination of adapter and task-specific prompts and the impact of V&L pre-training on adapters. 1