Previous data suggested that anastral spindles, morphologically similar to those found in oocytes, can assemble in a centrosome-independent manner in cells that contain centrosomes. It is assumed that the microtubules that build these acentrosomal spindles originate over the chromatin. However, the actual processes of centrosome-independent microtubule nucleation, polymerisation, and sorting have not been documented in centrosome-containing cells. We have identified two experimental conditions in which centrosomes are kept close to the plasma membrane, away from the nuclear region, throughout meiosis I in Drosophila spermatocytes. Time-lapse confocal microscopy of these cells labelled with fluorescent chimeras reveals centrosome-independent microtubule nucleation, growth, and sorting into a bipolar spindle array over the nuclear region, away from the asters. The onset of noncentrosomal microtubule nucleation is significantly delayed with respect to nuclear envelope breakdown and coincides with the end of chromosome condensation. It takes place in foci that are close to the membranes that ensheath the nuclear region, not over the condensed chromosomes. Metaphase plates are formed in these spindles, and, in a fraction of them, some degree of polewards chromosome segregation takes place. In these cells that contain both membrane-bound asters and an anastral spindle, the orientation of the cytokinesis furrow correlates with the position of the asters and is independent of the orientation of the spindle. We conclude that the fenestrated nuclear envelope may significantly contribute to the normal process of spindle assembly in Drosophila spermatocytes. We also conclude that the anastral spindles that we have observed are not likely to provide a robust back-up able to ensure successful cell division. We propose that these anastral microtubule arrays could be a constitutive component of wild-type spindles, normally masked by the abundance of centrosome-derived microtubules and revealed when asters are kept away. These observations are consistent with a model in which centrosomal and noncentrosomal microtubules contribute to the assembly and are required for the robustness of the cell division spindle in cells that contain centrosomes.