Some Accounting Books would describe Prepayments of expenses as expenses that are paid in advance in one accounting period, although the expenses relate to the next accounting period.
In Oracle Financials, could the expenses relate to the same accounting period as the accounting period the Prepayments of Expenses were made?

Sorry I did not understand the question completely.
There for usually two ways to handle prepayments.
1) When you make a prepayment you book it as an asset (lets say $100). When you receive an invoice (say for amount $20) you apply the prepayment. Prepayment entries are reversed and invoice expense comes into the picture. In other words you transfer the amount from prepayment asset to the invoice expense ($20). $80 are still remaining in your prepayment asset. They will be converted to expense when the prepayment is applied to future invoices.
2) You book prepayment amount (say $100) as expense because you are hoping to use all of that in the same period. You only received an invoice for $80. $80 was moved from prepayment expense to your invoice expense. Prepayment entries will be reversed by the system when you apply it to the invoice. You must move the remaining $20 into some asset account manually before reports are published. $20 must be represented in your balance sheet as an asset (and not in your income statement as an expense) because it is still an unapplied advanced payment which is conceptually an asset.
I hope that helps

Hasan, you did not understand my question.
My question was centered around the "Accounting Period" in regards to which one a Prepayment can be made and during which one (accounting period) the Prepayment can be applied. Some accounting text books say if the Prepayment is made in accounting period 1, its application can only take place in period 2 or later, not in the same accounting period 1.
Your above explanation tells me that in Oracle, the Prepayment and the application of the Prepayment can take place as well as in the same accounting period, or at a later accounting period , but not as the Text Books restriction on the application of the Prepayment.

Now I think, I understood your question. Thanks.
Oracle ERP (like any other enterprise scale ERP) is designed to be used by all kind of companies.
If your client follows such requirement than you can advice the client to enter settlement dates for prepayments; and keep the settlements date in the next period so that prepayment could not be applied in the current period.
But yes you are right. Oracle will let you apply prepayment even in the current period if you keep settlement date as system date.

Thank you, Hasan.