An improved two-stage dilute-acid hydrolysis process and apparatus the continuous saccharification of ligno-cellulosic biomass, or other cellulosic material feedstocks, with higher efficiency and better economics than known art, is disclosed. It comprises two double-tube heat-exchanger and plug-flow-reactor systems, in series. The improved process is primarily by reverse interstage transfer-flow, opposite to biomass, of second-stage surplus of: 1. process heat, 2. dilute- acid and 3. ingredient and solution water, all in an alpha cellulose hydrolysate, dilute-acid solution. It also comprises recycle of a fraction of unhydrolyzed alpha-cellulose hydrolysis residue, thereby achieving higher hydrolysis conversion of alpha-cellulose to glucose; and providing: 1. lower hydrolysate sugar decomposition, 2. reduced reaction time and 3. increased reactor processing capacity, without increased dimensions. The process is ideal for process control to efficiently produce a primary final liquid product, which is the combined hydrolysate sugars into a single solution, including pentose, hexose and glucose sugars, which are readily fermented into Ethanol and/or Torula Yeast. The secondary final solid product is the resulting net unhydrolyzed lignin residue solids.