By Air
Kenya Airways now flies direct from Nairobi, connecting with London and Paris flights. Yemenia Airways and Air Tanzania also fly to the Comoros.
By Boat
There are freighters that leave from Zanzibar and Madagascar. These are cheaper than flying, usually, but take longer and departure dates are less reliable. To catch these you must find the boat captain at the harbor and discuss prices. If you bargain very hard, you may get passage for 100 euros.