The detailed interactions of nitrogen oxides with ice are of fundamental interest and relevance for chemistry in cold regions of the atmosphere. Here, the interactions of NO, NO2, N2O4, and N2O5 with ice surfaces at temperatures between 93 and 180 K are investigated with molecular beam techniques. Surface collisions are observed to result in efficient transfer of kinetic energy and trapping of molecules on the ice surfaces. NO and NO2 rapidly desorb from pure ice with upper bounds for the surface binding energies of 0.16 +/- 0.02 and 0.26 +/- 0.03 eV, respectively. Above 150 K, N2O4 desorption follows first-order kinetics and is well described by the Arrhenius parameters E-a = 0.39 +/- 0.04 eV and A = 10((15.41.2)) s(1), while a stable N2O4 adlayer is formed at lower temperatures. A fraction of incoming N2O5 reacts to form HNO3 on the ice surface. The N2O5 desorption rates are substantially lower on pure water ice (Arrhenius parameters: Ea = 0.36 +/- 0.02 eV; A = 10(15.3 +/- 0.7) s(-1)) than on HNO3-covered ice (Ea = 0.24 +/- 0.02 eV; A = 10(11.5 +/- 0.7) s(-1)). The N2O5 desorption kinetics also sensitively depend on the sub-monolayer coverage of HNO3, with a minimum in N2O5 desorption rate at a low but finite coverage of HNO3. The studies show that none of the systems with resolvable desorption kinetics undergo ordinary desorption from ice, and instead desorption likely involves two or more surface states, with additional complexity added by coadsorbed molecules.