The phrase "asserted in their" is correct and usable in written English.
It can be used when referring to something that has been stated or claimed by a group or individual in their communication or documentation.
Example: "The findings were asserted in their report, highlighting the need for further research."
Alternatives: "stated in their" or "claimed in their".
But the traffickers asserted in their communique today that they believed they were talking with Government emissaries.
But lawyers for Mr. Schiavo, who is his wife's guardian, asserted in their brief that death was her desired outcome.
They asserted in their statement that the "driving force" in the transition from television to online video was "to have outstanding programs that people want to watch".
They asserted in their complaint, "Judith Terra owns a home in Washington, D.C., and desires to move the foundation there in order for her to obtain a prominent place in the social circles of Washington".
For example, even as a national controversy was developing over the planned execution of Gary Graham, the Texas Republicans asserted in their platform that "capital punishment should be swift and unencumbered".
But pharmacies and consumer groups asserted in their complaints to regulators that the two divisions of the company had shared consumers' records, steering people to the company's retail stores and mail-order operations, which gave CVS Caremark an unfair advantage over competitors.
The court's "intervention is necessary to preserve the integrity" of that decision, the Planned Parenthood lawyers assert in their petition.
In a world where funds are limited, that is just the kind of approach that is needed, Dr. Marvier and Dr. Kareiva assert in their American Scientist article.
Shareholders assert in their complaint that BP's management permitted violations of laws on environmental protection, worker safety and fair trade practices.
In response, corporate counsel will need to assert in their bylaw or charter provision that the action must be "necessarily" based on a "violation of a duty" to the corporation in order for reimbursement to be prohibited.
South African government officials said they were victims of a gold rush in cyberspace, asserting in their filing that Virtual Countries had tried to sell the domain name back to the country for a payment of $5 million to $10 million.
