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Abstract. For the random trigonometric polynomial N 2 s,(/)cosn0, n-l where g"(t), 0 < / < 1, are dependent normal random variables with mean zero, variance one and joint density functionwhere A/-1 is the moment matrix with py = p, 0 < p < 1, i ¥*j, i,j m 1, 2.N and a is the column vector, we estimate the probable number of zeros.1. Consider the random trigonométrie polynomial N (1.1) (9) = $(t, 9) =% gn(t) cos n9, where g"(t), 0 < t < 1, are dependent normal random variables with mean zero, variance one and joint density functionwhere M ~x is the moment matrix with pi} = p, 0 < p < 1, i =£j, i,j = 1, 2, . . . , N, and ä is the column vector whose transpose is 5' = (gx(t),..., gN(t)). In this paper we calculate the probable number of zeros of (1.1). We prove the following.Theorem 1. In the interval 0 < 9 < 2tt all save certain exceptional set of functions , where ex is any positive number less than 1/13.The particular case when p = 0, that is the case when gn(t) are independent normal random variables, was considered by Dunnage [3] and proved the following.

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