Starting in September 1998, NJ implemented a 2-year period for inspections.
The new inspection cycle was based on the model year of the vehicle, even or odd.
This resulted in 2000 stickers being issued to even-model-year vehicles in September through December 1998.

The inmplementation of this program was a bit unorthodox.
In September 1998, all cars went to inspection, odd-year cars got 1999 stickers, and even-year cars got 2000 stickers.
From October to December 1998, only even-year cars had to go to inspection (and got 2000 stickers).
For the entire year of 1999, only odd-year cars had to go to inspection (and got 2001 stickers).

Extension stickers for 1999 and 2000 were issued for cars that did not have to go to inspection,
and these extensions were for use with the regular 1998 and 1999 stickers.


Below is a table describing the sequence of events,
based on what sticker was on your car (and what model year your car was) in 1997.

vehicle model year	initial sticker on car in 1997	what happens for 1998 inspection	what happens for 1999 inspection	what happens for 2000 inspection	what happens for 2001 inspection
even	Jan-Aug 1998	go to inspection get 1999 sticker	get 2000 extension sticker in the mail	go to inspection get 2002 sticker	(nothing)
	September 1998	go to inspection get 2000 sticker	(nothing)	go to inspection get 2002 sticker	(nothing)
	Oct-Dec 1998	go to inspection get 2000 sticker	(nothing)	go to inspection get 2002 sticker	(nothing)
odd	Jan-Aug 1998	go to inspection get 1999 sticker	go to inspection get 2001 sticker	(nothing)	go to inspection get 2003 sticker
	September 1998	go to inspection get 1999 sticker	go to inspection get 2001 sticker	(nothing)	go to inspection get 2003 sticker
	Oct-Dec 1998	get 1999 extension sticker from the DMV	go to inspection get 2001 sticker	(nothing)	go to inspection get 2003 sticker

By the end of 2000, all vehicles had either a 2001 or 2002 sticker,
the inspection cycle for all cars was two years,
and the extension stickers were no longer in use.

A link to the press release from the New Jersey DMV describing this in detail is located here:
DMV Inspection Revisions Begin September 1

Proper use of the extension stickers was: 1999 extension on top of 1998 sticker, and 2000 extension on top of 1999 sticker.

Improper use of the extension stickers was inevitable, and caused some chaos.

And then there were the "normal oddities" as well.