An entirely new experimental method is described which enables the rate constants of neutral-neutral gas-phase reactions to be measured at ultralow temperatures. The measurements are made by applying the pulsed laser photolysis (PLP), laser-induced fluorescence (LIF) technique of studying the kinetics of free radical reactions in the ultracold-environment provided by the gas flow in a Cinetique de Reaction en Ecoulement Supersonique Uniforme (CRESU) apparatus. The experimental method is described in some detail and its application and limitations are discussed. Results are reported for the reactions of CN radicals with O-2 and NH3. For reaction (1) between CN and O-2 data are reported for the temperature range T=13-295 K and the rate constants are well-matched by the expression k(1)(T)=(2.49+/-0.17)X10(-11) (T/298)((-0.63+/-0.04)) cm(3) molecule(-1) s(-1). For reaction (2) between CN and NH3, rate constants cm in the temperature range T=25-295 K fit the expression k(2)(T)=(2.77+/-0.67)X 10(-11) (T/298)((-1.14+/-0.15)) Cm-3 molecule(-1) s(-1). The kinetic data are discussed in terms of the latest quantum chemical and reaction rate theories for these systems.