A stored-ion collision technique has been used to study the charge-changing collisions of multicharged nitrogen ions with ${\mathrm{H}}_{2}$ and ${\mathrm{N}}_{2}$ target gases. The ions were produced inside a Penning trap with use of electron-impact ionization. The time constants for exponential ion loss by charge-changing collisions were measured at several target-gas densities, and from these time constants and densities the rate coefficients for electron capture were calculated. For the collision of ${\mathrm{N}}^{3+}$ with ${\mathrm{H}}_{2}$, for which calculations by Gargaud and McCarroll were available, the cross section for electron capture was obtained from the rate coefficient using v\ifmmode\bar\else\textasciimacron\fi{}, where v\ifmmode\bar\else\textasciimacron\fi{} is the rms ion velocity. The relationships of the other measurements to available theory and to ion-beam measurements at higher energies are discussed. Rate coefficients were obtained at mean ion energies near 1.1, 1.65, and 2.3 eV for ${\mathrm{N}}^{\mathrm{q}+}$ charges q of 2, 3, and 4, respectively. The results of the rate coefficient determinations are k(${\mathrm{N}}^{2+}$,${\mathrm{H}}_{2}$)=[7.8(1.2)]\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$ ${\mathrm{cm}}^{3}$/s, k(${\mathrm{N}}^{3+}$,${\mathrm{H}}_{2}$)=[5.4(0.8)]\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}11}$ ${\mathrm{cm}}^{3}$/s, k(${\mathrm{N}}^{4+}$,${\mathrm{H}}_{2}$)=[4.2(0.6)]\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$ ${\mathrm{cm}}^{3}$/s, k(${\mathrm{N}}^{2+}$,${\mathrm{N}}_{2}$)=[2.6(0.3)]\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}9}$ ${\mathrm{cm}}^{3}$/s, k(${\mathrm{N}}^{3+}$,${\mathrm{N}}_{2}$)=[3.5(0.4)]\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$ ${\mathrm{cm}}^{3}$/s, and k(${\mathrm{N}}^{4+}$,${\mathrm{N}}_{2}$)=[2.0(0.3)]\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$ ${\mathrm{cm}}^{3}$/s.