A direct continuation of Tanoshii Moomin Ikka. 
 
In the remote and mysterious Moomin Valley live the Moomin trolls, gentle and peaceful creatures. Young Moomin and his family experience many strange adventures, both magical and mundane. Based on the children's stories by Tove Jansson. 
 
(Source: Anime News Network) 
 
Note: In several countries' releases these episodes are treated as part of the first season.

Farm life has never been this wacky. Where else could you find a turtle with a built in TV under his shell, a bald lion, an elephant whose trunk doubles as a garden hose and an inflatable octopus. All run by a good-natured ox named Olly.
 
(Source: Anime News Network)

Dommel is a lazy dog who does nothing more than eating and sleeping. His owner, Semafoor, is an inventor of the strangest things you could imagine. Together this becomes a mix for some funny events.
 
(Source: Anime News Network)

Alfred J. Kwak (Dutch, it takes place in The Netherlands) lost his parents, brothers and sisters when he was young. He was raised by a mole. The series covers the life of Alfred from the day he is born. In his life Alfred tries to help all sorts of animals all over the world. The series are meant to entertain children and teach them about life, covering historical events like World War II. 
(Source: AniDB)

Unusual things have been happening in Moominvalley. Moomin, Sniff and Mee leave for the Observatory on the Lonely Mountains to confirm the Muskrat's words: a comet is about to hit Moominvalley and destroy everything. On the way they meet Snufkin, the Hemulen and the Snorks and experience many adventures. 
(Source: Anime News Network)

In the remote and mysterious Moomin Valley live the Moomin trolls, gentle and peaceful creatures. Young Moomin and his family experience many strange adventures, both magical and mundane. Based on the children's stories by Tove Jansson. 
(Source: Anime News Network)

Telescreen BV