In both cases, a political cartoonist named Thomas Nast, publishing in Harper's Weekly in the early 1870s, can claim the credit.

A Donkey is the emblem for the Democrats. It goes back to presidential candidate, Andrew Jackson. His political opponents in 1828 tried to label him "jackass" for a populist manifesto, and what was seen as an excessively democratic slogan, "Let the people rule." Jackson was much more in tune with the voters, turning the whole thing to his advantage, and even put the donkey symbol on his own poster.

The donkey image for Democrats wasn't widely used, though, until 1870, when Thomas Nast put it one of his cartoons to represent an anti-Civil War group. It again struck a cord with the public and was soon the unofficial symbol of the party.

The Elephant became associated with Republican Party via another Harper's Weekly cartoon. Thomas Nast drew a donkey hiding under a lion's skin, scaring away zoo animals. One was an elephant, with bearing the label "The Republican Vote". Modern Republicans claim that Nast chose the elephant, because the animals are usually intelligent and steadfast, but scarey when riled.

 I guess one party is just an ass. Just kidding i don't know i would like to know that too.