Abstract : The evolution of magic numbers as a function of the neutron number for a given chain of isotopes is one of the major goals of nuclear physics today. Changing magic numbers may lead to profound modifications in the structure of exotic nuclei and manifest themselves experimentally in rapid changes of collectivity and shapes. In this thesis we have studied nuclei around 68Ni produced in deep inelastic collisions at GANIL. The nuclei of interest were selected and identified by the large acceptance VAMOS recoil spectrometer. Their structure was studied via the detection of the gamma rays emitted at the target point by the EXOGAM array. In one of the two experiments we also installed a specific setup dedicated to the measurements of the delayed gamma rays emitted by the nuclei after their implantation at the focal plane of VAMOS. In the first experiment we have observed a new isomeric state in 68Ni with a proton intruder configuration at an excitation energy which sensitively depends on the Z=28 and N=40 shell gaps. New transitions were also identified in odd-mass isotopes of Co, Fe and Mn. In the second experiment we have measured the lifetimes of the first-excited states in 63,65Co using the recoil distance Doppler shift method. From these lifetimes electromagnetic transition probabilities could be deduced, which in turn shed light on the collectivity of the studied isotopes. Comparisons with the shell model and with mean field calculations were carried and provided additional information on the proton-neutron interaction as well as on the evolution of the collectivity in this mass region.