[en] The probability theory is applicated to some problems arising at the description of the work of the modified counters with prolonging dead time. Using the method of the semirecurrent events the following problems are studied: the number of particles arrived at the counter during the dead time; the time length distribution between two successive registered particles; the joint distribution of the dead time and the idle period; the solution to the integral equation for the joint distribution in the discrete case; asymptotic properties; the approximate formulae; the idle period and the number of particles arriving during the dead time