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Limits on $\beta^+$EC and ECEC processes in $^{112}$Sn and on$\beta^-\beta^-$ decay of $^{124}$Sn to the excited states of $^{124}$Te havebeen obtained using a 380 cm$^3$ HPGe detector and an external sourceconsisting of natural tin. A limit with 90% C.L. on the $^{112}$Sn half-life of$0.92\times 10^{20}$ y for the ECEC(0$\nu$) transition to the $0^+_3$ excitedstate in $^{112}$Cd (1871.0 keV) has been established. This transition isdiscussed in the context of a possible enhancement of the decay rate by severalorders of magnitude given that the ECEC$(0\nu)$ process is nearly degeneratewith an excited state in the daughter nuclide. Prospects for investigating sucha process in future experiments are discussed. The $\beta^-\beta^-$ decaylimits for $^{124}$Sn to the excited states of $^{124}$Te were obtained on thelevel of $(0.8-1.2)\times 10^{21}$ y at the 90% C.L.

Search for $\beta^+$EC and ECEC processes in $^{112}$Sn and $\beta^-\beta^-$ decay of $^{124}$Sn to the excited states of $^{124}$Te