"I'm My Own Grandpa" (sometimes rendered as "I'm My Own Grandpaw") is a novelty song written by Dwight Latham and Moe Jaffe, performed by Lonzo and Oscar in 1947, about a man who, through an unlikely (but legal) combination of marriages, becomes stepfather to his own stepmother — that is, tacitly dropping the "step-" modifiers, he becomes his own grandfather.

In the song, the narrator marries a widow with an adult daughter. Subsequently, his father marries the widow's daughter. This creates a comic tangle of relationships by a mixture of blood and marriage; for example, the narrator's father is now also his stepson-in-law. The situation is complicated further when both couples have children. (Wikipedia)

Here's a version by Dennis Warner on YouTube: http://www.youtube.com/watch?v=W7x1ETPkZsk

Read also A Wonder of Relationship