After the week of shows in Puerto Rico, he re-appeared in Episode 1325, where he visited Oscar in New York, and then in Episode 1443, where he becomes an air steward for a Grouch airline. He continued to make recurring appearances over the next few seasons. In some episodes (including Episode 1682), it was established that Osvaldo had a pet dog named Peligro.
The Osvaldo puppet has the ability to move his eyes, and later was used as a background Grouch, sans nose as well as other Grouch characters (including Worby, Dr. Kvetch, Harry Bellagrouchy, and Spill O'Reilly). The puppet also appeared among the Sesame Street gang in A Muppet Family Christmas and Follow That Bird (used as Osvaldo and some background Grouches).
- Season 11: 1316, 1318, 1319, 1320, 1321, 1324, 1325, 1443
- Season 12: 1467, 1486, 1491, 1527, 1529, 1539, 1557
- Season 13: 1661, 1662
- Season 14: 1783, 1812, 1825
- Season 15: 1873
- Season 16: 2003
- Season 25: 3258
- In some books and scripts featuring the character, his name is spelled as "Oswaldo" instead.
- The Sesame Street Dictionary (1980)
- The Sesame Street Word Book (1983)
- Ernie's Finish the Picture (1985)
- Splish-Splashy Day (1989)
- What's in Oscar's Trash Can? and Other Good-Night Stories (1991) (as "Uncle Oswaldo")
- Oscar's Grouch Jamboree (1994)