Oscillations in active circuits enclosed in a cavity

i have designed an active multiplier and a driver amplifier circuit, now i want to integrate and keep it in a common package, how do i come to know that there exist any cavity oscillation once the package is closed? plz clarify

Since you don't specify the enclosure, I'll assume the simple case, which is a metal cavity (box). Assuming dimensions a, b, and c (in meters), relative permittivity = ε, relative permeability = μ, then the resonant frequencies for the Transverse Electric (TE mode) waves are given by:

where:
m = 0,1,2, ...
n = 0,1,2, ...
p = 1,2,3, ...
and m = n != 0
*From Advanded Engineering Electromagnetics, C.A. Balanis, 1989, pg. 390

Your lowest frequencies of resonance will be given when m, n and p are smallest (e.g 001, 010, 100 cases). If you assume that the cavity/package is acting as somewhat of a waveguide, then you should consider that the cavity may have "good" coupling characteristics at any frequencies above your lowest resonant frequency.

My concern is that how do i know that my cavity is oscillating, once the circuit is powered on ( means by measurement techniques)

you will need a clean signal source to power the RF input, and a spectrum analyzer to view the RF output

Like biff said, you'll see a poor output signal quality (compared to what you anticipate, or have measured with the circuit outside the pacakge). Besides spectral purity, check your power output, overall gain, noise figure, return losses, etc... all of the typical parameters you'd use to characterize the circuit.

May need a Spectrum Analyzer and a high-frequency probe, to see if there are oscillations inside of the cavity. These oscillations might not be able to be seen in a conducted test at the output (due to filtering), but they can degrade the efficiency of the frequency multiplier.