We consider scenario of the dark matter consisting of two fractions, stable part being dominant and a smaller unstable fraction, which has decayed after the recombination epoch. It has been suggested in Ref.[1] that the above scenario may alleviate tension between high-redshift (CMB anisotropy) and low-redshift (cepheid variables and SNe Ia, cluster counts) cosmological measurements. We derive constraints on the heavy relics branching to qq, e + e − , µ + µ − , τ + τ − , ν eνe , ν µνµ , W + W − and γγ in the above scenario by comparison of the secondary γ and ν fluxes produced by the process with recent diffuse γ and ν flux measurements.