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 natur
al 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.
The construction of an ion pulse ionization chamber aimed at measuring ultra-low levels of surface alpha-activity of different samples is described. The results of measurement carried out with alpha-source and copper samples and light-reflecting film VM2000 are presented.
