[en] We have studied the ''wrong-sign'' process D⁰→K⁺π^- to search for D⁰-D⁰ mixing. The data come from 9.0 fb^-1 of e⁺e^- collisions at √(s)≅10 GeV recorded with the CLEO II.V detector. We measure the relative rate of the wrong-sign process D⁰→K⁺π^- to the Cabibbo-favored process D⁰→K⁺π^- to be R=(0.332^+0.063_-0.065±0.040 )% . We study D⁰→K⁺π^- as a function of decay time to distinguish direct doubly Cabibbo-suppressed decay from D⁰-D⁰ mixing. The amplitudes that describe D⁰-D⁰ mixing, x^' and y^' , are consistent with zero. At the 95% C.L. and without assumptions concerning charge-parity (CP ) violating parameters, we find (1/2)x^'2<0.041% and -5.8%< y^'<1.0% . (c) 2000 The American Physical Society