An elastic holding member including a body provided with rigid portions and deformable portions each provided with a through hole, the member being intended for attaching a horological component to a support element and including an opening the contour of which includes three contact zones intended to come into abutment on the support element, the contact zones each being included on an internal face of a reception region of each deformable portion.

A fastening stud (1) for one end of a hairspring, the stud having a first portion (10) designed to come into contact with the hairspring, the first portion being formed such as to have a first surface (10b) and a second bearing surface (10c) with the hairspring.

A mechanical oscillating system for a clock including a balance spring manufactured from a non-metallic, polycrystalline material with a grain size between 10 and 50,000 nm, with a winding area of the balance spring 0.001 mm.sup.2 to 0.3 mm.sup.2, an oscillating body and a shaft for mounting of the oscillating body and the balance spring on the shaft. A spiral spring for a clock being manufactured from a non-metallic material, wherein the non-metallic material is a polycrystalline material with a grain size between 10 and 50,000 nm, and having a linear thermal expansion coefficient smaller than 810.sup.6/K.

An elastic securing organ for fastening a horological component on a support element including an outer peripheral wall capable of being connected to said horological component and an inner peripheral wall defining a triangular-shaped opening wherein the support element is capable of being inserted, the elastic securing organ includes elastic arms each forming one side of the triangular opening and helping ensure the gripping of the support element in the opening, each arm including: at least one cut-out defined completely or partially along the body of said arm, an elastic contact zone with the support element, and elastic peripheral zones which extend between this contact zone and the ends of this elastic arm, the contact zone having a greater quantity of material than the quantity of material forming each of the peripheral zones thereof.

The spiral includes turns of rectangular section, whose pitch p and/or thickness e can vary from the inside curve towards the outside curve, or whose winding can deviate from the line of a perfect spiral. The inside curve can also be extended by a self-locking washer for fixing the spiral on the balance arbour with no play. The spiral is manufactured by photolithography and galvanic growth, or by micro-machining an amorphous or crystalline material, such as a silicon wafer.

An assembly (300) includes (i) a hairspring (2) made of a paramagnetic alloy including at least one of the following elements: Nb, V, Ta, Ti, Zr and Hf, notably an alloy including the elements Nb and Zr with between 5% and 25% by mass of Zr and an interstitial doping agent including oxygen, and least one fastening part (1; 1), notably two parts (1; 1), in particular a stud (1) or a collet (1), for an end (2a; 2b) of the hairspring (2), the at least one part (1; 1) having a first portion (10; 10) that is designed to come into contact with the hairspring (2) and that is made of titanium or titanium alloy or of tantalum or tantalum alloy, notably grade 2 titanium or grade 5 titanium.

An elastic retaining member is for attaching a horological component to a support element. The retaining includes an opening into which the support element is capable of being inserted. The retaining member also includes rigid arms and elastic arms defined between the connection zones of the retaining member. The arms contribute to procuring elastic gripping of the support element in the opening, each rigid arm being provided with a single convex contact zone of the retaining member capable of engaging with a corresponding convex contact portion of the support element.

A one-piece balance spring includes a single strip wound on itself between an inner coil and an outer coil. The strip has a geometry such that when the angle of contraction of the balance spring has a value of 360 degrees, there is a constant distance between each coil from the second coil to the penultimate coil.

A one-piece balance spring including a single strip wound on itself between an inner coil and an outer coil, the strip having a geometry such that when the angle of contraction of the balance spring has a value of 360 degrees, there is a substantially constant distance between each coil from the inner coil to the penultimate coil.

A balance spring includes a strip wound around itself into several coils, the inner coil being integral with a collet including a band extending substantially in the form of a polygon. The outer contour on each bulging portion of the vertices of the polygon includes two axially extending walls substantially parallel to each other relative to the segment formed between the center of the collet and the end of the bulging portion.