Annet Kossen was born in Alkmaar and had her first job with the Dutch tourist board in Bergen aan Zee. She settled in Amsterdam at age 19, where she found employment as the secretary of the directors of subsequently the Carré Theater and the publishing house Querido. She moved to New York in 1964 and briefly attended the local School of Visual Arts. She worked as a saleswomen for New York based illustrators until returning to Holland with writer Rob Chrispijn in 1973.
She had made illustrations for a cookbook while in the States, and once back in Holland, she got more illustration assignments. She designed a children's stamp, and illustrated the original book starring 'Alfred Jodocus Kwak' by Herman van Veen. She created the comic characters 'Egel en Muis' for the educational magazine Okki. Casterman collected the stories in three books between 1993 and 1995. Kossen's porcupine and mouse became so popular, especially with young children, that she also featured them in a children's book. She additionally read her stories at elementary schools, and turned her story into a puppet-show. 'Egel en Muis' stories have been featured on the Dutch Sesame Street TV show, accompanied by songs by Kossen's husband Rob Crispijn.