ACSP means - Accepted, Settlement in Progress. When you send your cross-border SWIFT transfer it usually goes through one or several correspondent banks. Basically, if the payment is not credited to the beneficiary (ACCC status) and is not rejected by one of the banks in the chain (RJCT status), it is ACSP.
Usually, SWIFT payment should be delivered within 1 hour to 3 business days, but sometimes it takes longer. There could be different reasons for that, but the most common one is that it is under a manual review by the compliance specialist in one of the banks.
The manual review can be long. Compliance specialists don't have all the info, so they request the sender's bank or beneficiary's bank to provide details (like a copy of the ID or invoice, depending on the situation). That's why we develop SOWSOF, but it is another story.
If you have tracked the SWIFT payment here on TrackMySwift, it is in ACSP status, but there was no exact info on the particular bank which is currently reviewing your transaction than basically, we don't know the answer. The most correct way to get this info - is for the sender to ask his/her bank to provide a GPI payment tracking. This is a nice picture where you can see the whole route of the payment. Something like that:

Banks don't like to provide it, because often employees in the branch or the customer care department don't have an access to the SWIFT GPI Tracker tool. They rely on the payments department for that and don't want to bother them. So be insistent.
Sometimes a bank doesn't use GPI due to the cost savings. In this case, you can try to figure out the possible chain by using Payment Analysis. However keep in mind that this tool doesn't really track the payment, but build the potential routes by using information about Standard Settlement Instructions.
Usually, you can't contact correspondent banks directly. You should work on both ends with the sender's and beneficiary's banks.
In the meantime, you can check if there are any updates in our SWIFT tracker.
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