A detailed study of very neutron deficient nuclei with $Z\ensuremath{\simeq}40$ (Sr,Zr) and $N\ensuremath{\simeq}40$ has been carried out. Total potential energy surfaces taking into account both quadrupole and hexadecapole deformation have been calculated for the Zr ($Z=40$) nuclei, starting from the Nilsson model. Also oddmass nuclei have subsequently been studied when coupling the odd particle to the deformed even-even core. After extensive band mixing calculations for the $_{38}^{79}\mathrm{Sr}_{41}$ nucleus, comparison to the existing experimental data [energy spectra for positive and negative parity ${\frac{5}{2}}^{+}$ [422] and ${\frac{3}{2}}^{\ensuremath{-}}$ [301] bands; static moments $\ensuremath{\mu}$, $Q$; mixing ratios $\ensuremath{\delta}(\frac{E2}{M1})$ and branching ratios] has been carried out. We have also concentrated on the excited state properties of even-even Sr nuclei within the framework of the interacting boson model. A critical analysis of the interacting boson model parameters, as obtained from calculations in nearby nuclei, i.e., $_{34}\mathrm{Se}$, $_{36}\mathrm{Kr}$ is carried out, especially for the behavior of $\ensuremath{\kappa}$, ${\ensuremath{\chi}}_{\ensuremath{\pi}}$ and ${\ensuremath{\chi}}_{v}$.[NUCLEAR STRUCTURE Total potential energy surface calculations for even-even Zr nuclei ($36\ensuremath{\le}N\ensuremath{\le}60$). Band-mixing calculations for the adjacent odd-mass nucleus ($_{38}^{79}\mathrm{Sr}_{41}$). Band-state properties: [$\ensuremath{\mu},Q,\ensuremath{\delta}(\frac{E2}{M1})$, branching ratios]. Excited states in even-even Sr nuclei with $40\ensuremath{\le}N\ensuremath{\le}48$ in the interacting-boson model (IBA-2). Discussion of IBA-2 parameters. Calculation of quadrupole moments $Q({2}_{1}^{+})$, nuclear radii and isomer shifts.]