The magnetic properties and the low-temperature magnetic structures of the orthorhombic perovskite HoMnO3 (space group Pnma) have been studied on polycrystalline samples by magnetization, specific heat, and neutron diffraction measurements. By cooling, HoMnO3 exhibits three singularities at T-N = 41 K, T approximate to 26 K, and T approximate to 6.5 K, suggesting a rich magnetic phase diagram. The neutron diffraction data show that below T-N = 41 K, the Mn3+ magnetic moments become ordered in an antiferromagnetic arrangement, adopting a modulated sinusoidal magnetic structure characterized by the wave vector k = (k(x),0,0) (k(x) = 0.40 at 41 K) and defined by the magnetic mode (C-x,0,0). When the temperature is decreased, the propagation vector varies and at I approximate to 29 K a transition to a commensurate magnetic structure defined by k = (1/2,0,0) takes place. Below T approximate to 22 K, a small ordered magnetic moment appears on the Ho3+ cations, strongly increasing below 9 K and reaching 7.3(1) mu (B) at T = 1.8 K. The magnetic structure of the Ho3+ moments is defined by a (A(x),0,C-z) mode. The (H,T) phase diagram has been mapped out and the different magnetic structures interpreted on the basis of competing superexchange interactions.