Detailed Description:
  Try this.
---------
import java.awt.*;
import java.awt.event.*;
import java.io.*;

public class test {
  public static void main(String args[]) throws IOException {
    ObjectOutputStream oos = new ObjectOutputStream(
      new ByteArrayOutputStream());
    ScrollPane sp = new ScrollPane();
    sp.getHAdjustable().addAdjustmentListener(new AdjustmentListener() {
      public void adjustmentValueChanged(AdjustmentEvent ev) {}
    });	// this is key
    oos.writeObject(sp);
  }
}

12/7/99   xxxxx@xxxxx   -- explicitly remove the AdjustmentListener before
attempting to serialize the ScrollPane.


import java.awt.*;
import java.awt.event.*;
import java.io.*;

public class Test4085359
        implements AdjustmentListener, Serializable {

  public Test4085359() throws IOException {
    ObjectOutputStream oos = new ObjectOutputStream(
      new ByteArrayOutputStream());
    
        ScrollPane sp = new ScrollPane();

        sp.getHAdjustable().addAdjustmentListener(this);
	// adjustment listener kept as static variable by component/container,
	//	so no way to make it transient -- thus, remove explicitly
	//	before trying to serialize
        sp.getHAdjustable().removeAdjustmentListener(this);

    	oos.writeObject(sp);
  }
  
  public void adjustmentValueChanged(AdjustmentEvent ev) {
  }

  public static void main(String args[]) throws IOException {
        Test4085359 test = new Test4085359();
  }

}

In JDK 1.1.4, the result is 
java.io.NotSerializableException: java.awt.AWTEventMulticaster
        at java.io.ObjectOutputStream.outputObject(ObjectOutputStream.java)
        at java.io.ObjectOutputStream.writeObject(ObjectOutputStream.java)
        atjava.io.ObjectOutputStream.defaultWriteObject(ObjectOutputStream.java)
        at java.io.ObjectOutputStream.outputObject(ObjectOutputStream.java)
        at java.io.ObjectOutputStream.writeObject(ObjectOutputStream.java)
        atjava.io.ObjectOutputStream.defaultWriteObject(ObjectOutputStream.java)
        at java.io.ObjectOutputStream.outputObject(ObjectOutputStream.java)
        at java.io.ObjectOutputStream.writeObject(ObjectOutputStream.java)
        at test.main(test.java:13)

--------------------

12/7/99   xxxxx@xxxxx   -- A component's AdjustmentListener is kept as a static variable , so there's no way to make it transient (to allow comp to be serialized).
Not clear whether this is a bug, or a design decision made as part of the
fixes for 4027305.  The components that HAVE been made serializable are being documented as part of bug # 4085659.  I'm marking this as a dupe of 4085659.