On the 27th of April Ste. Suzanne withdrew his corps from its advanced position preparatory to recrossing the Rhine at Kehl. St. Cyr, having directed his artillery and trains to follow the river road on the right bank towards Schaffhausen, led his infantry across the hills towards St. Blazien. Moreau crossed the Rhine at Bâle with the reserve; one of his divisions, commanded by General Richepanse, then ascended the Weiss River, so as to join the right of St. Cyr's corps; the other two, commanded by Moreau in person, marched up the Rhine towards Schaffhausen.

On the following day Ste. Suzanne recrossed at Kehl, and proceeded up the left bank of the Rhine towards Brisach. St. Cyr, having united a part of his forces with Richepanse's division, occupied St. Blazien. Moreau himself forced a passage across the Alle River, and drove back an Austrian brigade there, which retreated towards Bonndorf.

On the 30th of April Ste. Suzanne, having arrived at Brisach, again crossed the Rhine to the German side, and took up the position at Friburg, at the entrance to the Höllenthal, recently occupied by St. Cyr's troops. St. Cyr remained in the vicinity of St. Blazien. Moreau advanced upon the Wutach River, and Lecourbe concentrated his corps on the south bank of the Rhine near Schaffhausen, preparatory to crossing the river at that point.

Thus the French corps continued to push forward. On the 1st of May Moreau reached Schaffhausen, where he was joined by Lecourbe's corps, part of which crossed the river in boats, and the remainder over a bridge temporarily constructed for the purpose. St. Cyr reached Stuhlingen, and Ste. Suzanne, having driven back the Austrian brigade occupying the Höllenthal, arrived at Neustadt.

During these movements the Austrian outposts along the Rhine fell back before Moreau to Stuhlingen, and, upon St. Cyr's arrival at that place, retreated upon Zollhaus. Meanwhile Kray had directed part of his own immediate command upon Loffingen and Zollhaus. Kienmayer, with the greater part of his forces, still remained in the valley of the Kinzig, and Starray in the valley of the Murg.

Thus the first part of Moreau's plan was successfully executed. As yet he had met with no reverse. His forces had driven before them the Austrian outposts and advance brigades, till now three of his corps, numbering eighty-five thousand men, were within supporting distance of one another on the north side of the Rhine near Schaffhausen. From this favorable position he could march at once against Kray in the Black Forest, and outnumber him almost two to one; for Kray could not expect immediate aid from his left wing, which was beyond Lake Constance on the borders of eastern Switzerland and in the Tyrol, or from his right wing, which was far away in the valleys of the Kinzig and the Murg.

Kray now began to appreciate the insecurity of his position. He perceived that his reserve and immense magazines at Stokach were in danger. Should Moreau capture this place and push rapidly forward towards Ulm, he would sever the Austrian communications, and thus place Kray in a position where a defeat would ruin his army. In order to prevent, if possible, such a result, Kray decided to unite his forces at Stokach, and there give battle to Moreau. With this end in view, Kray caused the following movements to be made. On the 2d of May the Austrian brigade that had been driven from Neustadt by the advance of Ste. Suzanne, moved to Bonndorf; the Austrians at Bonndorf marched to Zollhaus; and those at Zollhaus, to Geisingen, where Kray had collected the Austrian troops under his immediate command. On the 3d of May his columns advanced towards Stokach over the Geisingen-Engen road.

Meanwhile Moreau was not idle. On the 3d of May he moved on Engen with the reserve; St. Cyr on Zollhaus; and Lecourbe, having directed two brigades to ascend the Aach River, in order to connect with the right of the reserve, marched on Stokach with about twenty thousand men, attacked and defeated the twelve thousand Austrians there, captured the immense magazines, and forced the Austrians back towards Ulm by way of Mosskirch and by way of Memmingen. But after this victory Lecourbe, not receiving any orders from Moreau to push forward and seize Mosskirch, remained in the vicinity of Stokach, awaiting the result of the operations of Moreau at Engen.

Meanwhile Kray, on his way to Stokach, had reached Engen before the arrival of Moreau. In this position his troops, numbering about forty-five thousand men, faced south with their left at Engen and their right extended towards Zollhaus. Moreau soon arrived with the reserve. His forces, counting the two brigades on his right detached from Lecourbe's corps, numbered about forty thousand men. At once Moreau began the battle. Fiercely and desperately the French and Austrians fought for several hours, but neither gained a decided advantage. Finally, late in the day, St. Cyr, who had received orders from Moreau to hurry forward from Zollhaus, arrived and began an attack upon the right of the Austrians, which caused them to give way. But this attack was made too late to produce any decisive result. The Austrians, though forced at last to yield, were not crushed; in fact, Engen was little more than a drawn battle. But, during the night, Kray, having learned of the capture of Stokach, began to fear that Lecourbe would push forward, seize Mosskirch, and sever his communications with Ulm. He therefore decided to retreat. Leaving a rear guard to hold Moreau in check, he directed his forces upon Tuttlingen, Liptengen, and Mosskirch. At the battle of Engen each side lost in killed, wounded, and captured, about seven thousand men.

Kray now determined to unite as many of his troops as possible at Mosskirch, and there to make a stand against the French, who were pushing eagerly forward towards Ulm. Already he had sent word to General Starray and General Kienmayer to descend the left bank of the Danube, and join him at the earliest possible moment.