The company, formed recently after forking from ownCloud which was then forced to shut because it lost its US funding, said it had partnered with the HackerOne platform for this endeavour because of its wide take-up.
HackerOne has reported more than 24,000 bugs through the efforts of 3000+ hackers and it is popular among security professionals.
It is headed by former MySQL chief executive Marten Mickos.
"Reschke’s experience with open source and running competitive bug bounty programs at scale is sure to benefit Nextcloud security and its customers."
Bugs that are reported will earn fees from US$5000 downwards depending on the extent of their severity. Critical bugs that permit remote code execution on the server as an unauthenticated user will earn that amount.
Other categories of bugs and their respective bounties are high vulnerabilities (those that allow gaining of access to the complete data of another user - US$2000), medium (limited disclosure of user data or attacks granting access to a single user's user session - US$750), and low (very limited disclosure of user data or attacks involving a very high unlikely amount of user interaction - US$250).
Nextcloud community spokesman Jos Poortvliet said: "While we do perform internal research and add pro-active security hardening all the time (a prominent example being the introduction of same-site cookies) we are always looking for external input as well.
"Few limitations and exclusions as well as some of the highest rewards in the open source world for responsible disclosure will serve to attract the kind of professional expertise needed to turn this into a success.
"We’re confident in our codebase and our work and with this project we will bring the Nextcloud security to an even higher level."