A dual-mode electro-mechanical variable speed transmission includes an input shaft, an output shaft system, a gear system having at least three branches, two electric machines, and at least a clutch. The first electric machine couples to a branch of the gear system, the output shaft system couples to another branch of the gear system, the input shaft couples to the remaining branch or one of the remaining branches of the gear system, and the second electric machine selectively couples either to the same branch that is coupled to the output shaft system with a speed ratio or to one of the remaining branches that that is not coupled to the first electric machine with a different speed ratio. The transmission provides at least two power splitting modes to cover different speed ratio regimes. The transmission can also provide at least a fixed output shaft to input shaft speed ratio.