NOVELTY - The continuous production of biodiesel (I) from vegetable oils (II) of varying acidity involves: (i) heating (II) with (m)ethanol in the presence of a strong acid catalyst under pressure in a multiple, continuous, horizontal modular tubular reactor; and (ii) transesterifying the obtained (II), having acidity less than 1%, by mixing with sodium or potassium methoxide then separating the glycerol (III) formed from (I), which is suitable for use as fuel after purifying and scrubbing.    USE - Used for producing clean biodiesel (I), for use as a fuel in engines, especially for automobiles.    ADVANTAGE - (I) is obtained by a safe, versatile, continuous process from vegetable oils (II) (optionally replaced by animal fats) having a varying degree of acidity. The modular plant is easy to maintain, and the number of modules can be varied as a function of the industrial production capacity.    DETAILED DESCRIPTION - The continuous production of biodiesel (I) from vegetable oils (II) of varying acidity involves a first step (i) in which (II) is mixed with (m)ethanol at stoichiometric ratio 1:5-300 (based on free acids present) in presence of 1-10 g per kg of (II) of strong acid catalyst, in a multiple, continuous, horizontal modular tubular reactor. Each module, with capacity for 300-400 kg of (II), includes a tube for receiving (II); a centrally perforated plate system, with intermediate rod units for displacing the plates via a piston; a jacket for circulating water at 60degreesC; and a system for periodic evacuation of gases, water vapor and (m)ethanol, connected to the path for (II) between modules, controlled by electronic valves and assisted by injection of air, nitrogen or inert gas, the gases being passed from the top of the module to a distillation column in which water is stripped and alcohol is condensed. The modules are connected by multiway valves, allowing imput of reactants and air, exit of gases to the column and exit of (II) to the next module. Each module has a reaction control system, pressure and temperature sensors and a filling volume indicator, all integrated in an electronic circuit. The acidity of (II) is gradually reduced to less than 1%. In a second step (ii), the obtained (II) is mixed with sodium or potassium methoxide at stoichiometric ratio 1:6-50 at 45-60degreesC in a multiple vertical modular tubular reactor. Each module consists of a vertical tube containing fixed, extractable plates with central performations, through which oil is moved using a piston head. An antireturn valve and nozzle are provided, and descent of the pist head allows the starting materials to reach the main chamber, the vapors from which are evacuated via the top to a refrigerated pipe, condensed and recirculated. The product is evacuated via an upper opening to intermediate vessel for decanting the glycerol (III) phase, including a density or turbidity sensor to detect (III), the product being passed to the next module. (III) is passed through a heat exchanger to a vessel at 80degreesC, in which alcohol gases are separated, supported by injection of air, nitrogen or inert gas. (I) from the last module is heated to 80degreesC by heat exchange. Alcohols are separated and passed to a distillation column for recovery. (I) is purified and scrubbed in a vertical centrifuge, after which it is suitable for commercial use.    An INDEPENDENT CLAIM is included for (I) obtained by the process.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic diagram of the second (alkaline transesterification) stage of the process.    Transesterification module (18)    Fixed, centrally perforated plates (19)    Piston (20)    Motor (21)    Non-return openings in piston head (22)    Heating chamber (23)    Inlet line (24)    One-way valve (25)    Gas evacuation opening (26)    Cooled pipe for condensation of gases (27)    Condensed gas recycling line (28)    Openable cap, for cleaning the module (29)    Upper opening, for outflow of product (30)    Product outlet pipe (31)    Intermediate vessel, for decantation of glycerol (32)    Glycerol density or turbidity sensor (33)    Outlet tube of second module (34)    Glycerol collector (35)    Glycerol heat exchanger (36)    Glycerol receiver (37)    Pipe for supplying gases from glycerol receiver to distillation column (38)    Vertical centrifuge for purifying and washing biodiesel (39)    Biodiesel receiver (40)