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"of mutual exchange" is a grammatically correct phrase and can be used in written English.
It is typically used to describe a reciprocal or shared exchange between two or more parties. Example: "The two companies entered into a contract of mutual exchange, where they agreed to share resources and knowledge for the benefit of both parties."
Exact(11)
Meanwhile, with continuing globalization and the deepening of mutual exchange, the ties between the two regions will inevitably expand from the flow of people, goods and capital to other areas, influencing politics, culture and historical processes at large.
It was now about the virtue of mutual exchange.
This example also shows that the Americanisation of West German society after 1945 was a process of mutual exchange in which care packages played an important role.
In mid‑August, Governor Bull learned that p84 the two Settlements had held a joint meeting and had agreed on a desire for peace on the basis of mutual exchange of prisoners and the abandonment of Fort Prince George and Fort Loudon by the English.
6. Lack of mutual exchange: one way traffic in the giving department.
How you notice the other person, how you acknowledge the other person, how the other person notices you and acknowledges you... all constitute a kind of mutual exchange.
Similar(49)
From 1487 to 1490 a number of mutual exchanges can be documented.
First, people can easily recognize that additional kinds of mutual exchanges would serve their interests.
Through SUPER, which he says creates fertile ground for mutual exchange of scientific information, Trbalic was strongly supported as a guest student.
Leary was one of the first people to have a site on the world wide web, and that model of a mutual exchange of information is very much with us today.
If you asked older generations to define the word "socializing," they would likely describe something along the lines of "a mutual exchange of information, ideas and emotions". Generation X and those born before them socialized with each other in a variety of ways that created intimate relationships and made people feel connected to others — and still do.
More suggestions(19)
of dual exchange
of interpersonal exchange
of cooperative exchange
of equal exchange
of other exchange
of international exchange
of bilateral exchange
of mutual shares
of mutual slagging
of mutual contempt
of mutual interaction
of mutual overreaction
of mutual trust
of mutual suspicion
of mutual regard
of mutual disorientation
of civil exchange
of mutual brilliance
of mutual loathing
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com