New Zealand has 6 classes of drivers license, surprisingly numbered 1 - 6.
In order to get you class 2 you must have a class 1 (regular motor vehicle); to get class 3 or 4 you must have a class 2; to get class 5 you must have class 4. Class 6 is a motor cycle license and is separate.
The license levels relate to the maximum weight of the vehicle (including what it can carry) and the type - whether it is one rigid unit or a flexible combination of units (think truck and trailer).
You can also get endorsements on your license for driving particular kinds of vehicles that don't require an all-together new class of license. Taxi and bus drivers may get a "P" passenger license to show that they have consideration for the responsibility of carrying passengers. An "F" denotes forklifts.
For most small to average campervans and motorhomes available for rental, all that is required is a Class 1. The basic rule is that you can drive a vehicle up to 6000 kg, but there are several exceptions to this.
For larger vehicles that are rigid over 6000kg but under 18000kg, you need a Class 2. This may include some of the larger 5-wheelers depending on how much you have on board. It does apply to larger buses.
Class 3 is for vehicle combinations that weigh between 12000kg and 25000kg.
Class 4 is for rigid vehicles over 18000kg and Class 5 for combination vehicles over 25000kg. Passenger coaches are often Class 4, because when you think about it if they then are loaded with 35-45 people weighing an average of 80kg, then that is an additional 2800 - 3600kg, added to the luggage of perhaps another 700 - 900 kg, on top of a base coach weight around 18000kg.
For more specific information, see the New Zealand Transport Association website.
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