Unfortunately there is only rudimentary information about the concerts during these years.
Premiere at Famagusta
The live premiere of “ABBA” was abroad: all four were on vacation in Cyprus from April 5 to 16, 1970. They had an advertisement deal for these holidays with the travel agency Fritidsresor and part of it was a concert for Swedish UN soldiers. Rehearsals were done on the balconies of ABBA’s appartments at Twiga Tower.
None of the ABBA members seems to remember any part of the set list for this concert of about 15-30 minutes. It presumably included a mix of various Swedish songs. Probably two songs were done together as ‘pre-ABBA’.
In late 1970 and in spring 1971 Agnetha, Frida, Benny and Björn toured with a cabaret show, Festfolket, accompanied by the dance band The Lolas. This show was about 45 minutes. ‘Festfolket’ means ’party people’. There also was a joke about this name because when written as ‘Fästfolket’ it means ’engaged couples’. Rehearsals for this show began in September 1970 at the hotel (?) Sankt Jörgen.
Before the start of the tour they appeared on the radio show Våra favoriter (taped September 29, broadcast October 3) where they performed Frida’s Barnen sover, Agnetha’s Som ett eko and Björn & Benny’s Hej gamle man! from their upcoming solo album. On October 21 or 22 the TV programme Five Minutes Saloon was taped (broadcast December 13) with them performing on the songs Red Roses For A Blue Lady (chorus only) and California Here I Come. And on October 29-30 this was followed by the TV show I stället för Tarzan (broadcast October 31) possibly performing Hej gamle man!.
They usually performed on or around the weekends. According to Frida the audience varied from 14 to about 400. Especially the Festfolket shows were pretty disappointing and are remembered by the ABBA members as a big desaster, with people ordering their meals and raising their glasses to each other during the show.
This is the low end of the collaboration between the four of us. [...] Because we were not doing what we were supposed to do. We were singing other people’s songs in a kind of cabaret act. Benny and I were doing a number where we supposed to be two little boys. [...] It was embarrassing, but it was after that tour that we realized, our own songs that's we should do.
Björn in Sunday Night Show Special: Agnetha speaks, Channel 7, Australia, May 2013
It was not a success, generally comprising of a thin spread of vapid jokes and other people’s songs.
Agnetha, As I Am, p. 37
Luckily, the show was never recorded. This was when we learned exactly what we should not be doing.
[Hej gamle man!] got absolutely the best audience reaction of all the numbers in the show. That’s when we really knew that we should concentrate on doing our own material in the future – it was a kind of turning point.
The BAB tour
While Frida toured with Lasse Berghagen from May 1971 on, Agnetha, Björn and Benny did an own folkpark tour with 60 shows, starting on April 30. They performed cover versions and several of Agnetha’s songs during a show lasting for about 30-45 minutes, accompanied by Göran Lagerberg (bass) and Kjell Jeppson (drums).
A 1971 summer tour with all four together may have been dropped because of the long time they already had spent and would spent together so closely, in private as well as on stage, which caused some stress and quarrels amongst them.
Inbetween (on July 6) Agnetha and Björn got married, Björn & Benny worked on own projects and Agnetha recorded her album När en vacker tanke blir en sang during the tour.
It’s a charming show from the trio Agnetha, Björn and Benny. They are good on stage and Björn and Agnetha seem very loving as a couple. In total there are ten songs which are very chart-oriented, although some of the songs are quite weak. Most memorable is a superb version of Graham Nash’s Teach Your Children and two amusing sketches. Björn Ulvaeus still sings with a little nasal sound which is characteristic of him, whilst Miss Fältskog is still limited vocally. I’m sure that will change over the years...
Hans Fridlund in Expressen (according to ABBA The Book p. 53-54)
The show is sincere, simple and very “hit parade”. Agnetha Fältskog has more stage presence and sings more in tune now. Björn Ulvaeus got lots of applause for Hej gamle man and for his duets. As for Benny Andersson, he’s a real stage animal these days. But it looks like they’ve gone for the easy option. It’s a shame they don’t put more into different songs. Benny is one of our rare real composeres.
Bengt Malin in Aftonbladet (according to ABBA The Book p. 53-54)