What do the properties of the web  parts show? Do you have them both set
to be visible?

Some web parts  are smart in that if they don't have content, they don't
show up. Could that be the case?

I am confused on the question. Are you trying to get 2 web  parts to work this
way? Or is it working this and you do not want it to work this way?

Actually i have two webparts  which are included on my
dashboard. but for one of them i set the IsVisible property to False. That is
the reason when dashboard  renders it show only one webpart  whose IsVisible
property is set to true. Now i want to close  this web  part and open my another
webpart whose IsVisible property is false. so that i can see another webpart.
Also if i close this webpart then my previous web part  should show and this part
should get hide. means alternating the show hide of webpart but depending on
each others status.
I hope u got what i want to do. Example is
http://msdn.microsoft.com/library/default.asp

On this page if you close the left explorer view then you will get the Show TOC
button on top and if you click on show toc you will see the full explorer.
I hope this will help you in understanding my problem