The lifetime 7. of the 02 state in Kr has been measured by means of the Doppler shift attenuation method in gases. From the value of~and the measured value of the K-internal conversion branching Is(Oz~0,+)/Itt(Oz~2, +) the value of the electric monopole strength p (EO) of the 02 -+0, + transition has been deduced. Restriction or assignments for the spin parity of several levels in Kr, populated in the decay of Rb, have been deduced by measuring K-internal conversion coefficients of the relevant transitions. PACS number(s): 23.20.Nx, 21.10.Hw, 23.20.Lv, 27.50.+e As a part of a systematic investigation of the EO and E2 decay modes of 0+ excited states in even krypton isotopes, we recently reported some spectroscopic data on Kr concerning, in particular, the decay properties of the 02 state [I] In even krypton isotopes this state was interpreted by some authors [2] as belonging to the standard space of the interacting boson model in its IBM-1 version [3],while other authors [4], applying the IBM-2 model [3], interpreted it as an "intruder state, " i.e. , as lying outside the IBM model space. In Refs. [2,4] the comparison between experimental and calculated data relevant to 02 states was necessarily limited to excitation energies, due to the lack of experimental data on transition strengths from these states. In Ref. [1]we compared the available spectroscopic data on low-lying levels of Kr with the values predicted by the IBA-2 model, when a set of parameters different from that adopted in Ref.[4] is used. We found that it is still possible to give a consistent description both of excitation energies of the 02 state in these nuclei and decay properties of the 02 state in Kr, without introducing configurations lying outside the IBA-2 model space.In this paper we report on measurements in Kr concerning (i) the decay properties of the 1017 keV, Oz state, which could provide further support to the proposed description of the 02 states in Kr and (ii) the determination of several internal conversion coefficients, which enable us to assign the parity of several levels as well as to restrict the possible range of their spin values. This information is necessary for an analysis of the low-lying positive-parity levels of the even krypton isotopes (that we plan to perform in the near future) aimed at the identification of states having predominant mixed symmetry character under exchange of proton and neutron bosons [3]. The low-lying levels in Kr were populated in the P /EC decay of Rb [5] collected at the ISOLDE mass separator (CERN). The conversion electrons were analyzed by means of a compact magnetic transport system [6] coupled to a 5 cm x6 mm Si(Li) detector cooled down to the liquid nitrogen temperature. Under typical experimental conditions the energy resolution (full width at half maxi-mum) at 1 MeV was about 2 keV. Due to the large number of y rays in the decay of Rb, which generate considerable background in the silicon detector, it has been necessary to