Leslie,
Thank you for your question, and it’s a question that I get quite often.  The response time for a seller on a REO (Real Estate Owned) property can vary quite  a bit.  It seems that between the asset maangers representing these sellers and the listing agents marketing the properties … there are many different approaches to marketing the home.  I say this because how aggressively they price the home will play a big role in how many offers are submitted, which usually affects the response time.  Typically you’ll see between 3 days and 2 weeks for a seller response.  I know that is a big difference but it also depends on how many files that asset manager is trying to get off the bank’s books. 
To take it one step further, the way a seller will respond can vary also.  Sometimes the seller will just take the best offer to date … but sometimes they will send out a “multiple counter offer” to every buyer who submitted an offer, and give each buyer the opportunity to submit their “Highest and Best” offer.  This gives the buyer an opportunity to get a little bit more aggressive on their offer if they’d like to.
Hope this helps …  =)