Germany beat Brazil 3-2 in the men's Class 4-5 first round, while the Czechs defeated Slovakia 3-1.
In the men's Class 6-8, the Czech Republic team beat Sweden 3-2 and Germany overcame Slovakia 3-1. There was also a win for Spain.
Coach Hannes Doesseler said he was pleased with the German win as they felt Slovakia were the favourites going into the game.
He said: 'The Slovaks were the favourites, they are both Class 8 players while in our team we have two Class 7 and two Class 6 players.
'The Slovaks were favourites and we left them in that belief. We played very well against them. We played our best players against them but we have many tactical possibilities, although one of our players has problems with his shoulder.'
In the women's Class 4-5, Italy defeated Chinese Taipei 3-2 but Maria Nardelli was disappointed with her performance, praising team-mate Valeria Zorzetto.
She said: 'I played badly, I had a mental blockage, but Valeria played very well and kept us in the match... I had more confidence in the doubles because Valeria was playing so well, it meant I was able to free myself.'