The results of the experiment searching for 2K-capture with large low-background proportional counter are presented. The comparison of spectra of the background of the proportional counter filled with Kr enriched in $^{78}$Kr (8400 hr) and with natural Kr (3039 hr) is given. A new limit on the half-life of $^{78}$Kr with regard to 2K-capture, T$_{1/2}geq2.0cdot10^{21}$ yrs (95% C.L.) has been obtained.
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