Tremor is most common among the movement disabilities that affect older people, having a prevalence rate of 4.6% in the population older than 65 years. Despite this, distinguishing different types of tremors is clinically challenging, often leading to misdiagnosis. However, due to advances in microelectronics and wireless communication, it is now possible to easily monitor tremor in hospitals and even in home environments. In this paper, we propose an architecture of a system for remote health-care and one possible implementation of such system focused on head tremor monitoring. In particular, the aim of the study presented here was to test new tools for differentiating essential tremor from dystonic tremor. To that aim, we propose a number of temporal and spectral features that are calculated from measured gyroscope signals, and identify those that provide optimal differentiation between two groups. The mean signal amplitude feature results in sensitivity = 0.8537 and specificity = 0.8039 in distinguishing patients having cervical dystonia with or without tremor. In addition, mean signal amplitude was shown to be significantly higher in patients with essential tremor than in patients with cervical dystonia, whereas the mean peak frequency is not different between two groups.