The origins of the P-35 trace back to the Seversky SEV-3 three-seat amphibian, designed by Alexander Kartveli, Seversky's chief designer and Seversky's first aircraft. The SEV-3 first flew in June 1933 and was developed into the Seversky BT-8 basic trainer, 30 of which were ordered by the United States Army Air Corps (USAAC) in 1935. This proved grossly underpowered and was quickly replaced by the North American BT-9.
The second prototype SEV-3 was completed as a two-seat fighter derivative, the SEV-2XP. It was powered by a 735 hp (548 kW) Wright R-1820 radial engine, had fixed landing gear in aerodynamic spats and was armed with one .50 in (12.7 mm) and one .30 in (7.62 mm) forward-firing machine guns plus an additional .30 in (7.62 mm) gun for rear defence.
When the USAAC announced a competition for a new single-seat fighter in 1935, Seversky sent the SEV-2XP, confident it would win despite being a two-seater. However, the aircraft was damaged on 18 June 1935 during its transit to the fly-offs at Wright Field. To compete with the Curtiss Model 75, a single-seat aircraft with retractable undercarriage, Seversky rebuilt the aircraft into the single seat SEV-1XP, replacing the SEV-2XP's fixed landing gear with a retractable undercarriage where the mainwheels retracted backwards into the wing, and an 850 hp (634 kW) R-1820-G5 replacing the -F3 of the SEV-2XP. The SEV-1XP was delivered to Wright Field on 15 August for evaluation, which was generally successful, although the Cyclone failed to deliver its rated power and the SEV-1XP only reached 289 mph (465 km/h) rather that the 300 mph (483 km/h) predicted by Seversky.
Protests from Curtiss led to the formal flyoff between the fighters to be delayed until April 1936. The delay was used by both Seversky and Curtiss to improve their aircraft, while allowing additional fighters from Vought (the Vought V-141) and Consolidated with a single seat version of the PB-2. The SEV-1XP was re-engined again, with a two-row Pratt & Whitney R-1830-9 "Twin Wasp" replacing the Cyclone and a modified vertical stabilizer fitted, becoming the SEV-7.
The P&W also failed to deliver its rated power—it put out only 738 hp—and top speed was again well below 300 mph. While more expensive than the Curtiss and Vought designs, the Seversky was a clear winner of the Air Corps' competition, with an order for 77 P-35 fighters being placed on 16 June 1936. Modifications from SEV-1XP to production P-35 standard included partial instead of complete mainwheel fairings and seven degrees of dihedral to the outer wing panels.
The first production P-35 was delivered to the USAAC in May 1937, preceded by a company owned pre-production aircraft and demonstrator, the AP-1. Only 76 P-35s were built, delivery being completed in August 1938, with the 77th aircraft finished as the prototype XP-41. When it wanted further fighters in 1937, the Air Corps, who were unhappy with both the slow delivery of the P-35, and sale of 2PA two-seat aircraft to the Japanese Navy, ordered 210 Curtiss P-36s.
Seversky continued to develop the design with the hope of selling more aircraft both to the Air Corps and to civil and export customers. It modified the prototype SEV-1XP as a single seat racer, the S-1 entering it into the 1937 Bendix Trophy, where it finished in fourth place. The competition was won by the S-2 (registration number NR70Y), a similar aircraft built for Frank Fuller of the Fuller Paint Company. S-2 also won the Bendix Trophy in 1939 and placed second in 1938. The aircraft was used to portray the "Drake Bullet" in the 1938 film Test Pilot.
Another civil aircraft was the DS, (or Doolittle Special), a single seater for James Doolittle, employed at the time by the Shell Oil Company, while the AP-7 was another racer, powered by a 1,200 hp (895 kW) R-1830 engine and used by Jacqueline Cochran to win the 1938 Bendix Trophy race and to set a women's air speed record. Seversky entered two aircraft based on the P-35 in a 1938 competition for a new fighter for the Air Corps. One was the XP-41 (which had the company designation AP-4D, which was a P-35 with a 1,200 hp (895 kW) R-1830-9 engine fitted with a two-stage supercharger and the AP-4, which had a turbo-supercharger mounted in the belly of a deeper fuselage. The Air Corps preferred the AP-4D, which was ordered into production as the P-43 Lancer.
Aiming to increase sales, Alexander P. de Seversky personally took a demonstrator on a tour of Europe in early 1939. As a result of this demonstration, Sweden ordered 15 EP-106 fighters on 29 June 1939, a development of the P-35 powered by a 1,050 hp (783 kW) R-1830-45, which improved performance by over 25 mph (40 km/h) and armed with two 7.9 mm (.311 in) machine guns in the cowl and two 13.2 mm (.52 in) machine guns in the wings. A second order for 45 EP-106s was placed on 11 October 1939, with a third order for 60 aircraft, placed on 6 January 1940, although by this time Seversky had been thrown out of the company bearing his name by the board of directors, with the company renaming itself Republic Aviation. The Swedish Air Force designated them J 9.
Nonetheless, despite its obsolescence as a fighter design, the P-35 design served as the inspiration for the promising Italian Reggiane Re.2000 Falco fighter which bears a superficial similarity in layout.