Hi Desmond,

As I dont know whats the exact way you doing
So I feel only one way

Select the object which you want to keep vissible and to set actionsettings
for mouse over and run this function

Sub PrepareVissibleShape()
With ActiveWindow.Selection.ShapeRange(1)
   .Visible = msoTrue
   .Name = "VissibleObj"
   .ActionSettings(ppMouseOver).Action = ppActionRunMacro
   .ActionSettings(ppMouseOver).Run = MakeShapeVissible
End With
End Sub

Now Select the shape which you want to make invissible and run this macro
Sub PrepareInvissibleShape()
With ActiveWindow.Selection.ShapeRange(1)
   .Visible = msoFalse
   .Name = "InvissibleObj"
End With
End Sub

Also keep this macro in the same module
Sub MakeShapeVissible()
Dim sh As Shape
For i = 1 To ActivePresentation.Slides(1).Shapes.Count 'Change Slide index
accrodingly
   With ActivePresentation.Slides(1).Shapes(i)
       If .Name = "VissibleObj" Then
           .Visible = msoFalse
       ElseIf .Name = "InvissibleObj" Then
           .Visible = msoTrue
       End If
   End With
Next i
End Sub

Now you try slideshow and see if it works.
Check this website if you don't know where to write VBA code
http://pptfaq.com/FAQ00033.htm

Does it have to be a mouseover? A triggered animation is likely to be more
reliable but this would have to be a click.

Can you explain " .... on another slide" though. If you need an object to
appear on a DIFFERENT  slide then it would have to be vba.

Using vba to set the visible property can cause problems with other
animations and also once set to true or false it will stay that way next time
you run the presentation unless you write code to initialise it how you want.

tutorials on triggers
http://www.pptalchemy.co.uk/powerpoint_hints_and_tips_tutorials.html#triggers