In 1969, 5 ulpans operated in Leningrad. In autumn of the same year, Mark Dymshits, engineer and former military pilot, began learning Hebrew at one of the ulpans. Two months later, he proposed to Gilel Butman, one of the managers of the organization, that they not wait for permissions from the authorities to leave for Israel but, instead, hijack a plane and leave the USSR. The idea was extreme, but it was not rejected. They began considering options. They rejected immediately hijacking an Antonov-2 aircraft that took off from Erevan. In case of success, there would be no resonance, whereas the purpose was not just to get out of the USSR, but to attract the world's attention to the state of Jews in the USSR: that those who wished to repatriate themselves were kept by force within the country and that Jews were assimilated by force.
The second variant was discussed for longer. They proposed hijacking a Tupolev-124 or Tupolev-134 aircraft. All the passengers were supposed to be members of the Leningrad or Riga organizations, including Eduard Kuznetsov and his wife Silva Zalmanson. It was most suitable to hijack a plane leaving for Murmansk. They wanted to reach Stockholm. When they arrived there, they planned to give a press-conference about the state of Jews in USSR. The world's opinion was supposed to make their governments pressure the USSR in order to attain permission for all Jews to leave for Israel. They planned to buy the tickets in different booking-offices under neutral names. The explanation of their recognizable appearance was supposed to be simple: they were going to a wedding. So, the action got the name "Wedding Operation". During the flight, Mark Dymshits was to penetrate to the cockpit and to make the pilots change course by threatening them with a self-made pistol; in case of their refusal, he was to pilot the plane himself.
When the plan of the operation was developed in detail, the date was set - May 2, 1970. However, at the beginning of April, the conference of the organization decided to reject the hijacking of a plane. Dymshits did not obey the decision and continued to ready the operation together with its Riga participants. They adjusted the plan. A new flight appeared in the timetable of the local airlines of Smolnoye airport - to Sortavala via Priozersk. The Antonov-2 aircraft could seat 12 passengers and only Riga men could fill it up. The operation was set for June 15, 1970. The plan was to make the pilots give up the controls, land the plane in Priozersk, have the pilots disembark there (after giving them tents and sleeping-bags), take on 4 more participants, and fly to Stockholm. The group was equipped, in addition to the pistol, with a hatchet, ropes and gags. These things allowed the authorities to accuse the group later of preparing a terrorist action. Near the plane ramp, KGB officers arrested the group.
Immediately, arrests began in Leningrad, Riga and Kishinev. During the investigation, Brazinskas and his son hijacked a plane to Turkey, killing a stewardess and injuring two pilots. This fact complicated the position of the group accused of the Zionist plot. In Leningrad, in the City Court, two trials took place: one of the group that prepared to hijack the plane and other of the Committee of a Zionist organization. The sentences for the former were more severe. E. Kuznetsov and M. Dymshits were sentenced to death, the others - to long terms of imprisonment. However, the trial generated a great deal of press in the West ant the death sentences were shortly after replaced with 15-years imprisonment; the sentences of the others were shortened.
Nevertheless, the desperate attempt to hijack a plane had some effect. In 1971, Jews who had appealed for permission to leave for Israel began getting the permission. The authorities let them go cautiously and refused them at any possibility, using such excuses as their knowing state secrets and so on. Nevertheless, while the participants of the "Plane Case" and other Jewish activists served their sentences, planes from Leningrad, Moscow and other Soviet cities to Vienna or Budapest took Jewish repatriates and emigrants out of the USSR. The members of the Zionist circles of the 1960s managed to make a breach in the wall. In 1979-1981, the participants of the trials of 1970 were deported to Israel in exchange for Soviet agents exposed in the West.