SrMn2P2 and CaMn2P2 are insulators that adopt the trigonal CaAl2Si2-type structure containing corrugated Mn honeycomb layers. Magnetic susceptibility X and heat capacity versus temperature T data reveal a weak first-order antiferromagnetic (AFM) transition at the Néel temperature TN = 53(1) K for SrMn2P2 and a strong first-order AFM transition at TN = 69.8(3) K for CaMn2P2. Both compounds exhibit isotropic and nearly T-independent X(T ≤ TN), suggesting magnetic structures in which nearestneighbor moments are aligned at ≈120° to each other. The 31P NMR measurements confirm the strong first-order transition in CaMn2P2 but show critical slowing down above TN for SrMn2P2, thus also evidencing second-order character. The 31P NMR measurements indicate that the AFM structure of CaMn2P2 is commensurate with the lattice whereas that of SrMn2P2 is incommensurate. These first-order AFM transitions are unique among the class of (Ca, Sr, Ba)Mn2 (P, As, Sb, Bi)2 compounds that otherwise exhibit second-order AFM transitions. This result challenges our understanding of the circumstances under which first-order AFM transitions occur.