Nuclear inheritance is highly ordered, ensuring stringent, unbiased partitioning of chromosomes before cell division. In plants, however, little is known about the analogous cellular processes that might ensure unbiased inheritance of non-nuclear organelles, either in meristematic cell divisions or those induced during the acquisition of totipotency. We have investigated organelle redistribution and inheritance mechanisms during cell division in cultured tobacco mesophyll protoplasts. Quantitative analysis of organelle repositioning observed by autofluorescence of chloroplasts or green fluorescent protein (GFP), targeted to mitochondria or endoplasmic reticulum (ER), demonstrated that these organelles redistribute in an ordered manner before division. Treating protoplasts with cytoskeleton-disrupting drugs showed that redistribution depended on actin filaments (AFs), but not on microtubules (MTs), and furthermore, that an intact actin cytoskeleton was required to achieve unbiased organelle inheritance. Labelling the actin cytoskeleton with a novel GFP-fusion protein revealed a highly dynamic actin network, with local reorganisation of this network itself, appearing to contribute substantially to repositioning of chloroplasts and mitochondria. Our observations show that each organelle exploits a different strategy of redistribution to ensure unbiased partitioning. We conclude that inheritance of chloroplasts, mitochondria and ER in totipotent plant cells is an ordered process, requiring complex interactions with the actin cytoskeleton.