Problem with the Phase of a transfer function

Dear Matlab users,

I have a strange problem which I am unable to figure out. I have a continuous system consisting of three subsystems having transfer functions f1(s), f2(s) and f3(s). Since, these subsystems are in series, the overall transfer function of the system is:

y(s) = f1(s)*f2(s)*f3(s)

[Multiplication in frequency domain and NOT the convolution]

I can get the response of this function using FREQRESP function and extract the phase using ANGLE function. My problem is:

ANGLE(y(s)) ~= ANGLE(f1(s)) + ANGLE(f2(s)) + ANGLE(f3(s))

[~= means NOT EQUAL TO]

According to my understanding, the frequnecy response of the three transfer functions is complex, so the phases should add.

Can someone please indicate where is my logic wrong??