Near the end of the 19th Century, a new dance came to dominate the fashionable ballrooms. It was an evolution of the Polka called the Two-Step. It was (from the leader's perspective) Left-Together-Left-Aaaaad-Right-together-right (Quick-Quick-Quick-Slow-Quick-Quick-Quick) taking up a single phrase of 4/4 music. It was, essentially, a Polka without the hop.
For over a decade, from the middle 90s until around 1910, most fashionable dance programs were a mix of Waltzes and Two-Steps. Polkas, Mazurkas and Schottisches had disappeared, and Quadrilles which had once dominated the dance programs were few or non-existent.
The Two-Step could be fast or medium or slow, generally the steps were small, it could move in a line or rotate, and the actual dance was fairly simple, with few variations or flashy moves. The Two-Step never really went away. It persisted until the age of Jazz and was quietly subsumed into the Foxtrot. It was however pushed out of the limelight by later dances like the Turkey Trot, One-Step and Foxtrot.
Here's what a Tw0-Step looked like in execution.