In Java, access specifiers are used to control the visibility and accessibility of methods and variables in classes and interfaces. The access specifiers for methods in interfaces are public and default.

Public methods in interfaces can be accessed by any class or interface that has implemented the interface. These methods are part of the public API of the interface and are meant to be used by external code.

Default methods, on the other hand, are only accessible within the interface or by classes in the same package as the interface. They provide a way to add new methods to an existing interface without breaking backward compatibility with existing implementations.

It's important to note that prior to Java 8, interfaces could only declare public abstract methods. However, with the introduction of default methods and static methods in Java 8, interfaces can now have concrete implementations as well.

In summary, the access specifier of methods in interfaces in Java can be either public or default, and they determine the visibility and accessibility of the methods to external code and classes within the same package.