1 Introduction

Most $\delta$ Scuti stars show multiperiodic radial or non-radial variations. Besides, many $\delta$ Scuti stars, such as 4 CVn, show strong amplitude variability of some modes from year to year, while the frequency remains essentially constant. The behavior of the amplitude variability differs from mode to mode. Even though resonances or near resonances among the excited nonradial pulsation modes of variable stars are considered as a possible cause for amplitude variation in $\delta$ Scuti variables, no satisfactory explanation or theoretical modelling have been available so far. The problem of how the amplitude varies is still open.

DQ Cephei(= HD 199908 = BD + 55$^\circ$ 2452), discovered by Walker in 1951 (Walker 1952), was one of the first known $\delta$ Scuti stars. In 1953, Walker proposed a period of $0\hbox{$.\!\!^{\rm d}$}07886$. This period is equivalent to a frequency of 12.6904 cycle per day, and was confirmed by the radial velocity study conducted by Sahade et al. (1956). Fitch organized larger scale observations in 1958 and drew the conclusion that there possibly exists two pulsation frequencies: 12.6799 and 8.0516 cycle per day (Fitch et al. 1965). In order to accurately determine the periodic variations of DQ Cephei, Pena (1983) organized a two-site photoelectric photometry collaboration in 1981. The analysis of their data provided two frequencies 8.0603 and 12.6788 cycle per day, which fits well to observations covering a time span of twenty nine years. However, in all these observations, the amplitude of the mode near 8.0603 cycle per day is small and the signal/noise ratio is not high enough to confirm its existence.

When checking the observational results, and leaving aside the mode near 8.0603 cycle per day which needs further confirmation, we find some evidences for amplitude variations of two pulsation modes during a 29 years time span. In order to identify the two pulsation modes and to study in detail the amplitude variations during a 46 years period, we organized new observations and present the results as follows.