Recently, many r e a l i s a t i o n s o f r e l a x a t i o n q u a r t z c r y s t a l o s c i l l a t o r s have appeared. They are simply designed and a r e i n s e n s i t i v e t o l o a d and temperature v a r i a t i o n s . A l s o , t h e y have a small number o f components and t h e i r s h o r t -t e r m f r e q u e n c y s t a b i l i t y i s good. O p e r a t i n g p r i n c i p l e o f q u a r t z m u l t i v i b r a t o r i s known i n t h e l i t e r a t u r e , b u t t h i s knowledge i s insuf f i c i e n t f o r a n a l y s i s o f o s c i l l a t i n g c o n d i t i o n , o s c il l a t i o n b u i l d i n g up and p e r i o d . These c a l c u l a t i o n s are performed using topological methods o f g e n e r a l theory o f r e l a x a t i o n o s c i l l a t i o n s , t h a t i s b y phase plane analysis.F i r s t , g e n e r a l e l e c t r i c a l and mathematical models of q u a r t z r e l a x a t i o n o s c i l l a t o r s a r e e s t a b l i s h e d . Then, phase p o r t r a i t o f c r y s t a l m u l t i v i b r a t o r i s cons t r u c t e d . Recently, many r e a l i s a i ns of r e l a x a t i o n q u a r t z o s c i -I l a t o r s have appeared They are simply designed and a r e i n s e n s i t i v e t o l o a d and temperature v a r i a t ions. Also, they have a small number o f components. T h e i r s h o r t -t e r m f r e q u e n c y s t a b i l i t y i s good9. A q u a r t z m u l t i v i b a t o r o p e r a t i n g p r i n c i p l e i s known i n t h e 1 iterature'. The q u a r t z c r y s t a l u n i t i s e x c i t e d by a voltage step-function generated by some c u r r e n tc o n t r o l l e d s w i t c h . As a response the current through t h e c r y s t a l i s g e n e r a t e d i n t h e f o r m o f a "harmonic o s c i l l a t i o n " . I n t h e s t e a d y -s t a t e , t h e a m p l i t u d e o f t h e q u a r t z c u r r e n t i s s t a b i l i z e d on the value neces s a r y f o r s w i t c h i n g on and o f f o f t h e c u r r e n t -c o n t r ol l e d s w i t c h . Such an approach provides a p o s s i b i l i t y f o r an i n t u i t i v e c o n s t r u c t i o n of v a r i o u s q u a r t z m u l t i v i b r a t o r c i r c u i t s , b u t does n o t e n a b l e i n v e s t ig a t i o n o f t h e o s c i l l a t i o n s t a r t i n g , t h e o s c i l l a t i n g frequency and i t s s t a b i l i t y . All t h e s e r e s u l t s may be obtained by the use o f t h e g e n e r a l o s c i l l a t i o n t h e o r y o f r e l a x a t i o n o s c i l l a t i o n s . T h i s method i s used i n t h e p r e s e n t p a p e r f o r t h e q u a r t z m u l t i v i b r at o r a n a l ys i s. Our present discussion will be organised as f o l l o w s I n f i r s t s e c t i o n , t h e g e n e r a l e l e c t r i c a l and mathemat i c a l model o f t h e q u a r t z -c o n t r o l l e d m u l t i v i b r a t o r s i s developed. I n second s e c t i o n , t h e t y p i c a l phase p o r t r a i t o f t h e q u a r t z c r y s t a l m u l t i v i b r a t o r s i ...