N.M. Stat. § 19-10-22
All oil and gas leases issued by the commissioner of public lands prior to the effective date of this amendment which have not expired, or which have not been legally canceled for nonperformance by the lessee or assignee, are hereby declared to be valid and existing contracts with the state of New Mexico according to their terms and provisions, and the obligation of the state and of the commissioner to observe and conform to the terms and provisions thereof is hereby recognized. In any case where two or more persons claim a valid lease on the same tract or tracts of land under the provisions of this section, then the rights of the conflicting claimants shall be determined by the commissioner subject to right of appeal from the decision of the commissioner as provided by law.
The legal owner and holder of any lease or leases issued by the commissioner prior to March 12, 1929, if not in default of any of the provisions thereof, may relinquish the same to the state and upon application filed at the time of filing such relinquishment, the commissioner shall issue the applicant a new lease upon the form prescribed by Section 2 of this act. The primary term of the new lease issued pursuant to such relinquishment shall be the unexpired term of the original lease and as long thereafter as oil and gas in paying quantities, or either of them, is produced from the leased premises by the lessee, and the new lease shall provide for the payment of the annual rental prevailing in the district wherein the lands affected are situated, but not less than the rental provided in the original lease. In converting such lease, as herein provided, the commissioner shall prescribe a reasonable filing fee for the filing of the relinquishment and application, and the lessee shall not be required to pay any rental in addition to the rental provided in the lease relinquished for the current year in which the lease is relinquished, except the difference, if any, between the amount of rental provided in the old lease and that to be provided in the new lease. The provisions of Chapter 125 of the 1929 Session Laws [19-10-1, 19-10-12 to 19-10-25 NMSA 1978], and of this act [19-10-1, 19-10-12, 19-10-15 to 19-10-18, 19-10-22 NMSA 1978] relating to sales of leases within a restricted district upon competitive bidding, or by sealed bids, or at public auction, shall not apply to this section.
NMS § 19-10-22