5.  Mrs Anita Švarc was born in 1968 and lives in Vuzenica. Ivan Kavnik was born in 1956 and lives in Topolščica. 6.  On 30 October 1989 the applicants were injured in a car accident in Austria. The accident resulted in the premature birth of their son, who sustained in utero injuries in the accident. The son died in hospital in Slovenj Gradec (Slovenia) on 28 December 1989. The perpetrator of the accident had taken out insurance with the insurance company Wiener Allianz Versicherungs Aktiengesellschaft (“WA”). 7.  On 27 October 1992 the applicants instituted civil proceedings against WA in the then Celje Basic Court, Velenje Branch (Temeljno sodišče v Celju, Enota v Velenju), seeking damages of 3,237,900 Slovenian tolars for the injuries sustained in the car accident and the non-pecuniary damage sustained following the death of their son.
On 4 January 1993 Mr Lojze Ude, a professor at the Faculty of Law in Ljubljana, delivered an expert opinion in the case at the request of WA. He stated that the Slovenian courts had no jurisdiction to examine the applicants' claims. At the time, Mrs Dragica Wedam-Lukić was a work colleague of Mr Ude.
On 6 January 1993 WA lodged preliminary written submissions arguing that the case was not within the court's jurisdiction. They attached the opinion prepared by Mr Ude to the submissions, which were included in the file and served on the applicants.
On 25 May 1993 Mr Ude was appointed as a justice at the Constitutional Court (Ustavno sodišče).
On 22 February 1994 the Celje Basic Court, Velenje Branch, held a hearing.
On 18 and 25 February 1994 the applicants lodged preliminary written submissions contesting Mr Ude's opinion and WA's arguments.
On 22 April 1994 a decision dated 22 February 1994, the date on which the hearing was held, was served on the applicants. The court decided that the case was not within its jurisdiction, but made no explicit reference to Mr Ude's opinion.
 8.  On 4 May 1994 the applicants lodged an appeal with the Celje Higher Court (Višje sodišče v Celju).
On 28 June 1994 the Convention took effect with respect to Slovenia.
On 23 August 1994, on a request by the Celje Higher Court, the first-instance court delivered a supplementary decision concerning the costs of the proceedings.
On 1 September 1994 the applicants appealed against the decision concerning costs.
On 14 December 1994 the Celje Higher Court dismissed both applicants' appeals. 9.  On 14 February 1995 the applicants lodged an appeal on points of law with the Supreme Court (Vrhovno sodišče) against the decision of 14 December 1994.
On 27 February 1997 the Supreme Court dismissed the appeal on points of law against the judgment of 22 February 1994 and rejected the appeal against the decision of 23 August 1994 as inadmissible. 10.  On 22 May 1997 the applicants lodged a constitutional appeal with the Constitutional Court (Ustavno sodišče). In their appeal, they made no reference to Mr Ude's opinion.
On 1 April 1998 Mrs Wedam-Lukić was appointed as a justice at the Constitutional Court.
On 24 March 2000 the Constitutional Court declared the appeal inadmissible as manifestly ill-founded. Mr Ude was the president of the three-judge bench which examined the admissibility of the case and Mrs Wedam-Lukić was also a member of that bench. The applicants learned of the composition of the panel on 20 April 2000, the date on which the decision was served on them.