Agnetha appeared with Ola Håkansson and sang Fly Like The Eagle and The Way You Are during Flyktinggalan (Gala for Refugees), a charity event where viewers were asked to call a phone number and donate money.

At the end line-up, Agnetha can be seen with the rest of the cast standing and singing next to Peter Cetera.  The tune is that of Auld Lang Syne.

The two presenters were Håkan Hagegård and Kjell Lönnå.  Other guests included Carola, Howard Jones and:-

1. Emilio Ingrosso and Pernilla Wahlgren – Paradise
2. Lena Philipsson – Cheerio

It was at this show that Agnetha met Peter Cetera as he was on the same show singing Glory Of Love. As they were fans of each other, Agnetha and a few of her friends went out to dinner with Peter and that's when they began talking about possibly working together in the future.  Of course this resulted in Agnetha's I Stand Alone album, released in 1987.

Click here for a TV guide from Grimstad Adressetidende – 4 October 1986, p.15.

Flyktinggalan 86 (Agnetha), 1986;
Flyktinggalan 89 (Benny), 1989;

Archive data from Swedish Media Database:
SVT, TV1 1986-10-04
Fullständig tablå
19.00 Barnjournalen.
19.30 Flykting-gala 86.
Tablåinnehåll TVB86-1216
21.00 Aktuellt och väder.
21.15-22.00 Flykting-gala 86.
Utgivning
År/datum 1986-10-04
Kanal SVT1
Utgivning Stockholm : SVT, TV1
Utgivningsland Sverige
Exemplar
VHS TV87-0643
1 tum B LP TVB86-1216
MPEG-1 ZS_svt_svt1_1986-10-04
MPEG-2 YA_TV87-0643

Thanks to Daniel Johansson, Robin Andersson, Dustin, Jozsef, Pascale Ranson and Claes Davidsson for lots of information (most of it via ABBAMAIL (no longer online)).
YouTube link c/o Rosa Mannen and Secret Service