Long-period (LP) events have been widely observed in relation to magmatic and hydrothermal activities in volcanic areas. LP waveforms characterized by their harmonic signature have been interpreted as oscillations of a fluid-filled resonator, and mixtures of liquid and gas in the form of bubbly liquids have been mainly assumed for the fluid. To investigate the characteristic properties of the resonator system, we analyse waveforms of LP events observed at four different volcanoes in Hawaii, Alaska, Colombia and Japan using a newly developed spectral method. This method allows an estimation of the complex frequencies of decaying sinusoids based on an autoregressive model. The results of our analysis show a wide variety of Q factors, ranging from tens to several hundred. We compare these complex frequencies with those predicted by the fluid-filled crack model for various mixtures of liquid, gas and ash. Although the oscillations of LP events with Q smaller than 50 can be explained by various combinations of liquids and gases, we find that ash-laden gases are required to explain long-lasting oscillations with Q larger than 100. The complex frequencies of LP events yield useful information on the types of fluids. Temporal and spatial variations of the complex frequencies can be used as probes of fluid composition beneath volcanoes.