Recently, in several countries including South Korea, the percentage of households having fixed telephones, which is often called the fixed telephone coverage rates, has decreased due to a rapid spread of mobile phones. It is generally assumed that the lower the rates of coverage, resulting in a major frame undercoverage problem, the greater the possibility of the bias. In this paper, we first take a look at the changes of coverage rates in both fixed telephones and mobile phones in South Korea and examine the coverage rates by sociodemographic characteristics of households. Also, we refer to a change in the level of fixed telephone noncoverage and the resulting problems in the situation. Second, we provide a comparison of the coverage rates for households for some European countries, the United States, Canada etc. Finally, we suggest further research to rise to our research environments increasingly troublesome, owing to the wide spread of mobile phones.