When you make an offer on a REO, the bank's asset manager, not the listing agent, makes the decision on how the offers are handled. Even if you are told your offer is being accepted, it is not binding until both buyer and the bank's representative have both signed and initialed the contract AND all riders and addendums. It sometimes takes days or even weeks for the bank to get a fully signed contract back to the buyer's agent. During that waiting period, other offers can come in. Each bank sets their own policy as to how additional offers will be handled. Your offer should be accompanied by a Proof of Funds letter if paying cash or your Pre-Approval letter from your lender if getting financing.
When you do get an offer accepted by the bank on a REO property, the bank/seller will generate it's own addendums to the contract, which the buyer must accept without changes in order for the transaction to move forward. These addendums frequently alter the inspection period, modify the sellers warranties to reduce seller's liability, add mold or other environmental disclaimers and frequently change deadlines within the contract. Often they include language that makes the buyer's deposit nonrefundable after the inspection period. There's typically a disclaimer that buyer is responsible for obtaining any HOA or condo docs at buyer's expense. Most have specific waivers of certain buyer rights, such as filing legal action against the bank for failure to close (specific performance). They also put language in that allows the seller, at seller's sole discretion, to extend the expiration date on the contract.
For all of the above reasons, it's a good idea to seek out your own real estate attorney that is familiar with REO sales to review the bank's addendums with you BEFORE you sign and accept the terms.
Find an agent that is experienced with REO sales to guide you through the process