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In order to serialize an object within an ArrayList that is modified during program execution, you will need to follow these steps:

1. Implement the Serializable interface in the class of the object that you want to serialize.

2. Define an ArrayList object to store the objects that you want to serialize.

3. Add the objects that you want to serialize to the ArrayList object during program execution.

4. Use the ObjectOutputStream class to serialize the ArrayList object, which will also serialize the objects within it.

5. Upon deserialization, the objects will be read in the same order that they were written, so you will need to ensure that the order of the objects within the ArrayList is consistent.

6. If you modify the ArrayList during program execution after serialization, and you want to save the changes in the serialized file, you will need to serialize the ArrayList again with the modifications.