The two groups were kept some distance apart by barriers and a heavy police presence in Horse Wynd outside the Scottish Parliament.
Police said four people were arrested for minor offences during the day and that disruption was kept to a minimum.
The demonstrations, which have now finished, involved a march by the SDL from East Market Street down part of the Royal Mile. The group, which included people holding English Defence League banners, carried signs saying "Support Our Troops" and "Stop Foreign Aid".
They chanted slogans as they made their way down Canongate, flanked by Police Scotland officers in fluorescent jackets.
Anti-fascism and anti-racism campaigners took part in a counter-protest.
They gathered earlier in the day in Chambers Street and appeared to outnumber those in the SDL group.
The gathering of individuals and organisations included members of Unite Against Fascism.
During their demonstration near the Scottish Parliament, they chanted slogans such as "SDL off our streets" and played music.
According to police estimates, around 130 SDL members and supporters were involved in the events and around 350 took part in the anti-fascism protest.
Officers from across Scotland provided a "significant presence" in the city centre to ensure the events passed peacefully, police said. They were set to continue high-visibility patrols throughout the evening.
"Robust planning with our partners was undertaken to ensure those wishing to protest could do so, while at the same time allowing daily business within the city to continue as normal," said Chief Superintendent Mark Williams, divisional commander for the city.
"I would like to praise the Edinburgh public for their continued support and assistance throughout today."
The protests took place during the height of the city's festival season with the International Festival, Festival Fringe and International Book Festival all in full swing.