0 used to refer to something that will happen or be done on the next day:
1 used to describe a service that supplies something the day after it is ordered:
Our premium service guarantees next-day delivery.
It is certainly not meeting its obligation on next-day delivery of first-class mail.
The uniform price and next-day postal service delivered nationwide are a fundamental commitment.
To ensure next-day delivery, night flights are necessary.
If a customer goes to a post office, there are already similar post office services which assure next-day delivery.
He says that there is a very high next-day delivery record for first-class mail.
We are providing a next-day delivery of first-class mail in 94 cases out of 100.
That service, mainly for commercial matters, costs £13 per item for guaranteed next-day delivery.
In many other areas, the obligations on next-day delivery of first-class mail are not being met.