In this paper, we describe an algorithmic framework for the automatic detection of diffraction-limited fluorescent spots in 3D optical images at a separation below the Rayleigh limit, i.e. with super-resolution. We demonstrate the potential of super-resolution detection by tracking fluorescently tagged chromosomes during mitosis in budding yeast. Our biological objective is to identify and analyse the proteins responsible for the generation of tensile force during chromosome segregation. Dynamic measurements in living cells are made possible by green fluorescent protein (GFP)-tagging chromosomes and spindle pole bodies to generate cells carrying four fluorescent spots, and observe the motion of the spots over time using 3D-fluorescence microscopy. The central problem in spot detection arises with the partial or complete overlap of spots when tagged objects are separated by distances below the resolution of the optics. To detect multiple spots under these conditions, a set of candidate mixture models is built, and the best candidate is selected from the set based on chi2-statistics of the residuals in least-square fits of the models to the image data. Even with images having a signal-to-noise ratio (SNR) as low as 5-10, we are able to increase the resolution two-fold below the Rayleigh limit. In images with a SNR of 5-10, the accuracy with which isolated tags can be localized is less than 5 nm. For two tags separated by less than the Rayleigh limit, the localization accuracy is found to be between 10 and 20 nm, depending on the effective point-to-point distance. This indicates the intimate relationship between resolution and localization accuracy.