Yes, whether you have lived in Delaware for many years and have just moved out of state or you are visiting for a short time, you can apply for a non-resident card for a fee. The fee to obtain a library card for non-residents is different depending on the county you are applying in. In Sussex and Kent counties, the fee for non-residents is $25*. In New Castle County the fee is $40. You will still need to fill out the application and bring or mail it to any local branch, along with the fee and a photo ID.
If you are a non-resident but own property or work* in Delaware, you are eligible to receive a Delaware library card.
Registration forms:
*depending on local library policy