Kiwibank says it is having problems with processing transactions and accessing people's accounts.
It says no phone banking or internet access was available for two short periods on Wednesday, while ATM and eftpos access are available but only with cleared funds.
Kiwibank says it has an emergency team working on the issue, but there is a possibility that interbank transactions will not be processed and available to customers on Wednesday night.
The bank says it will try and ensure people will have access overnight to their wages, salaries and benefits.
Meanwhile, BNZ says a computer glitch which has resulted in some Visa transactions occurring multiple times may have been happening over the past week.
A spokesperson says the bank is working on building a clearer picture of the problem.
She says the bank is trying to move quickly to reverse any duplicate transactions, as well as any bank fees that may have been incurred as a result.
Various New Zealand banks have experienced computer difficulties over the past two months.
Last week, ASB encountered a technical glitch that delayed overnight payments to some customers.
In April, some public sector employees were not paid due to a problem with a payments messaging system.