The article discusses some problems that have arisen in the field of civil and arbitration proceedings generated by the threat of the spread of coronavirus infection in the territory of the Russian Federation in late March – early May 2020. Subjects of civil procedural and arbitration procedural relations were faced with insurmountable circumstances restricting the right to access to justice. The situation is considered from the point of view of the principle of judicial proceedings within a reasonable time, the principle of procedural economy, legality. The category «cases of urgent nature» is analyzed, the correctness of its use in judicial practice is questioned. The question is raised about the independence of judges and their subordination only to the Constitution of the Russian Federation and federal law as a guarantee of the right to an independent and fair trial. The threat of the spread of coronavirus infection on the territory of the Russian Federation entailed a violation of the rights and legitimate interests of persons participating in cases in civil and arbitration proceedings. It was revealed that civil disputes (in the broad sense of the word) at the end of March – beginning of May 2020 were left without proper attention from the courts; the courts were unable to promptly respond to the current situation, effectively carry out their functions, and provide large-scale remote access to justice.