Are Newton's laws applicable for 2 bodies in the same inertial frame moving with a very high velocity (close to $\rm c$)? If two bodies are in same inertial frame and are moving with very high velocity  (close to $\rm 3×10^8\ m/s$) but slightly different in magnitude, then can we apply newtons law in case of these two bodies?
 A: If you do an experiment in a lab and it follows Newtonian mechanics to a high precision, then the same experiment in a lab moving uniformly with any velocity should give rise to the same results. This is straight from the principle of relativity.
Of course, outside observers will see a lab subject to strong relativistic effects. But the question was what happens in the lab frame moving with the bodies where their relative velocities are very subrelativistic.
A: Firstly, objects aren't "in" a frame of reference. The frame of reference is where you choose to analyze the situation from. So I will assume you mean

are newton's laws applicable to 2 objects moving at relativistic velocities relative to you that are nearly equal to each other?

Newtonian mechanics is a limiting case of relativistic mechanics and is applicable to objects that have a velocity relative to your chosen frame of reference that is much smaller than c i.e whether or not you can apply newtonian mechanics depends on your chosen frame of reference.
Note, however, unlike in newtonian mechanics, due to time dilation and length contraction, the time interval between 2 events, the distance between 2 points, the relative velocity between 2 objects, inertia of objects ....etc.... can change depending on the frame of reference you choose from, so you must take this all into account when doing a coordinate transform
A: The answer depends upon what you mean by 'apply' Newton's laws.
Clearly Newton's laws apply to everyday circumstances on Earth. In the frame of a passing muon, however, relative to which the Earth is moving at close to the speed of light, the application of Newton's laws to everyday events on Earth will produce unrealistic results.
