We have carried out detailed structural, magnetic and thermal properties studies of the Mn(Se, S) system. The detailed structural studies using synchrotron X-ray and neutron diffractions on MnSe confirm the coexistence of cubic and hexagonal phases at low temperature, which shows strong thermal hysteresis suggesting the first-order nature of the transition. Based on the temperature-dependent magnetic susceptibility, we confirmed that the substitution of the sulfur element to selenium critically modified the complex magnetism observed in MnSe. It was to our surprise to observe a magnetic anomaly at 16 K way below the antiferromagnetic order that sets at about 160 K in MnS. Our neutron study at low temperature did not reveal any additional magnetic structure below 16 K. However, the specific heat of MnS shows a clear T1.5 temperature dependence below 16 K, suggesting the possible emergence of a weak ferromagnetic order.