I'm not sure if the home you have put in an offer on is a home that is in the process of being foreclosed on, or if it is a bank owned property (often referred to as an REO). Also, if it is in the process of being foreclosed (pre-foreclosure), are the offers for more than the loan (s) amount or less. If less then it is a short sale (selling the home for less than is owed on the home).
For a short sale, the bank will often want the homeowner to negotiate the offer/offers and present the "best" offer to the bank. Sometimes in a short sale the bank will want to be involved in the negotiation of the offers, but usually they just want the "best" offer presented to them.
For an REO, you'll be negotiating directly with the bank and usually they are looking for the strength of the offers and may take a long time.
If it is a short sale, you'll want to be sure that the seller's real estate agent has been in contact with the bank and has secured approval to sell the home short and has had ver recent discussions with the bank about the current market condition.
If the home is being sold for more than the loan amount, you'll want to be sure that if your offer is accepted, that the bank is aware of the offer, closing date etc.
In any of the above, you'll want to have your attorney involved through the whole process AND you'll want to have an attorney who specializes in real estate AND is familiar with foreclosures.
I will say that as in most dual offer situations, cash is king...if you are a cash buyer, you trump every other kind of buyer and you are in the driver's seat. If your offer is not a cash offer, you must include a strong letter of pre-approval from a large lender. Bigger earnest money amounts, quicker closing dates and fewer contingencies are things that help with the strength of the offer. The highest offer doesn't always win, especially in a foreclosure. A cash buyer with a short closing date and not contingencies is a dream buyer in the foreclosure world and can get a price discount!
In summaray, as Michael says, there are too many complexities to cover here. Find professionals (realtor and an attorney) and get their help.
Look for a Certified Distressed Property Expert (CDPE) to help you.