The Alfine 11-speed is oil-lubricated, but the other Nexus and Alfine hubs are packed with a special grease as sold. Mechanical problems can result from "preventive maintenance" including re-lubrication with incorrect grease. This is especially the case if a hub has a coaster brake, due to the heat this brake generates.
The hub must be disassembled into its major components, solvent cleaned, dried and re-lubricated.
Metal wear particles contaminate the grease, and so the hubs require periodic cleaning and replenishment of a special grease that does not make the pawls stick. Still, frequent failures of grease-lubricated hubs due to water contamination have been reported in wet climates --see photos here. Conversion to oil lubrication avoids this problem and also allows replenishment of the lubricant without dismantling the hub.
More information about oil lubrication is in the main file about internal-gear hubs.
Dismantling the Nexus and Alfine hubs is not as difficult as you might think, because of their modular construction.
If you unscrew everything that is screwed onto the left end of the axle, the whole mechanism can be pulled out of the right side as a unit.
These hubs have a rotary shifter rather than a shifter rod in a hollow axle, and so you can't add oil by squirting it into the end of the axle. To replenish oil between rebuilds, you must either unscrew the left bearing cone (which requires removing the wheel from the bicycle) or else add an oiling port, such as a Sturmey-Archer oil cap.
A Shimano Rollerbrake is lubricated without any disassembly, using the special Nexus brake grease -- there's a small rubber access plug on the side of the brake unit, just pop off the plug, put the nozzle of the grease tube up against it, and squeeze.