The storm may have passed, but its effects on big banks and their customers are far from over.

Many big bank offices and branches remained closed on Tuesday afternoon, as companies planned their recovery from Hurricane Sandy.

Some New York companies reported flooding in their downtown offices, and indefinite power and public transit outages in the city threatened to disrupt business for much of the week. Many banks promised to waive fees or otherwise help customers caught in the storm’s wake.

JPMorgan Chase (JPM) said Tuesday it will continue waiving or crediting fees related to overdrafts or late loan payments through Thursday, for customers in ten states and the District of Columbia.

Spokesman Tom Kelly said JPMorgan Chase would start to reopen closed branches on Wednesday, "ensuring it is safe for employees to get to work and we have access and power — either utility or generator."

Bank of America (BAC) opened some Northeast branches on Tuesday, but branches in New York City, northern Virginia and several other affected states were still closed. The bank’s offices at the World Financial Center in Lower Manhattan and many of its wealth management offices in the storm's path remained closed.

Spokesman Mark Pipitone said Bank of America would refund fees incurred because of the storm, if customers contact the bank. "We will also refund fees for customers using other bank's ATMs to withdraw cash in the hardest hit states if contacted," he added.

Citigroup (NYSE: C) is "ready to provide financial recovery solutions for customers impacted by the storm, including access to cash and waiving fees," spokeswoman Shannon Bell said in an email Tuesday.

Some of Citigroup’s downtown New York offices have been flooded and one of them, at 111 Wall Street, "will remain unavailable for several days," according to a Citi memo to employees. Other downtown offices have also been flooded but should reopen by the end of the week, according to the memo.

Citigroup is hoping to reopen some Northeast branches, including those in Washington, by Tuesday afternoon. The memo said it will decide later today whether it can open branches in the New York area and other affected states on Wednesday.

Wells Fargo closed more than 770 Northeast and mid-Atlantic branches on Tuesday, according to spokeswoman Sara Hawkins. "We will determine hours for Wednesday based on the storm's impact through today," she said in an email Tuesday afternoon.

The San Francisco bank said Monday that continuing through Thursday it would waive or credit late fees on credit card payments, consumer and small business loans for customers in seven Northeastern states and Washington, D.C., who have been affected by the storm.

Wells Fargo also said it would waive fees for customers in the region who use another bank’s ATM, and has encouraged homeowners in the storm’s path to contact the bank about options for paying their mortgages and handling property insurance claims.

American Express (AXP) emailed customers on Tuesday morning, telling them that "American Express is here for you if you need emergency financial, medical or travel assistance." The credit card company also posted a message on its website offering to help affected customers who contact it by phone or by Twitter.

Spokeswoman Marina Norville said in an email that the credit card company is "assisting customers traveling to or from the area helping to rearrange travel plans and ensure they can travel when transportation is up and running." American Express will also "provide assistance" and offer "flexible payment options" for affected credit card customers who have problems paying their bills on time.

Capital One (COF) also will waive fees or otherwise help affected customers who contact the bank, according to an email from spokeswoman Amanda Landers.