Unfortunately there are no markings on the uniforms typical of the shoulder patches the military wears today. That was the practice in the early days of WW1.
The best I can give you an educated guess:
I would be inclined to say they are U S Army for these reasons:
The officers are wearing what were called Sam Brown Belts. That was a belt worn on the outside of the jacket with an additional strap going up and over the right shoulder. They were generally symbolic of an officer rank as they had no practical purposes (for example holding up the pants).
The lack of patches makes the picture most likely either before or in the first year or so of WW1. General Black Jack Pershing instituted the typical shoulder patch we know today when he got to Europe. Interestingly his superiors made him take them all off. They were afraid that advertising the unit they were with would give the enemy tactical and troop movement information. Pershing successfully got them to reverse their decision by showing that the patches gave the unit a sense of cohesion and unity which greatly raised their morale.
The style of boots with the pants legs tucked into up to the knees was typical of the cavalry uniform. However that does not mean that these are necessarily cavalry troopers as they were also worn by regular infantry troopers as well. Generally only the army wore these style of boots as only the army had genuine cavalry troops. In fairness, the marines do have a cavalry unit but they are generally only a few troopers and usually only perform color guard and ceremonial duties.
Hope this helps.
And again I want to emphasis that without patches or flags the best I can give is an (educated) guess.
"Laissez-faire capitalism (AKA The Great Material Continuum) is the only social system based on the recognition of individual rights and, therefore, the only system that bans force from social relationships." ~ Ayn Rand
