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DE will tax you for income earned in DE regardless of the dates.

Since you have TX income, you would file Nonresident. DE instructions state "Part-year residents electing to file a non-resident return – This option may be advantageous if, during the period of non-residency, you had any income from other states or sources outside of Delaware."

Please see the DE Instructions for more information.

The DE return for non-residents does not ask for dates in DE. Currently, DE is not available online. This link will keep you updated for availability.

Since you are military, be sure to answer the military question in the personal section, My Info, as seen below.

The program will then ask questions depending on your answers to create an accurate return.

Be sure to mark TX as your home of record. The program will ask where else you made money.